{"id":2360,"date":"2020-07-29T07:34:16","date_gmt":"2020-07-29T07:34:16","guid":{"rendered":"https:\/\/blog.prepbytes.com\/?p=2360"},"modified":"2022-03-28T01:34:04","modified_gmt":"2022-03-28T01:34:04","slug":"fear-of-heights","status":"publish","type":"post","link":"https:\/\/prepbytes.com\/blog\/fear-of-heights\/","title":{"rendered":"Fear of Heights"},"content":{"rendered":"<p><img decoding=\"async\" src=\"https:\/\/prepbytes-misc-images.s3.ap-south-1.amazonaws.com\/assets\/1645098958242-Article_313.png\" alt=\"\" \/><\/p>\n<h3>CONCEPTS USED:<\/h3>\n<blockquote>\n<p>Computational geometry.<\/p>\n<\/blockquote>\n<h3>DIFFICULTY LEVEL:<\/h3>\n<blockquote>\n<p>Medium.<\/p>\n<\/blockquote>\n<h3>PROBLEM STATEMENT(SIMPLIFIED):<\/h3>\n<blockquote>\n<p>For any triangle ABC we know that the height from A to the line BC(or it&#8217;s extension) is Ha, from B to the line AC (or it&#8217;s extension) is Hb and from C to the line AB (or it&#8217;s extension) is Hc. Now you are given these three values and you have to figure out the area of the Triangle ABC.<\/p>\n<p>If the triangle ABC is not possible for the given Ha,Hb,Hc. Print &quot;IMPOSSIBLE&quot;.<\/p>\n<\/blockquote>\n<p><a href=\"https:\/\/www.prepbytes.com\/panel\/mycourses\/mentors-coding-program\/c++\/week\/24\/computational-geometry\/codingAssignment\/FOHEIGHT\" title=\"Go to mycode.prepbytes.com\" target=\"_blank\" rel=\"noopener noreferrer\"><u><strong><\/strong><\/u><\/a><\/p>\n<h4>For Example :<\/h4>\n<pre><code>Input\n4\n31.573 22.352 63.448\n46.300 50.868 86.683\n22.005 24.725 22.914\n5.710 25.635 32.805\n\nOutput\n1517.456\n2219.941\n311.804\nIMPOSSIBLE<\/code><\/pre>\n<h3>SOLVING APPROACH:<\/h3>\n<blockquote>\n<p>You can find the area of a triangle if you know the length of the three sides by using Heron\u2019s Formula. It seems almost logical that something along the same lines could be used to find the area if you know the three altitudes.<\/p>\n<p>Let the sides of the triangle be a, b, and c. The altitudes to the sides are the heights used to find the area of the triangle. Let the altitudes to sides a, b, and c be called ha, hb, and hc.<\/p>\n<p>The area of the triangle can be found by 1\/2 a ha or 1\/2 b hb or 1\/2 c hc.<\/p>\n<p>a ha = b hb = c hc<\/p>\n<p>a\/b = hb\/ha<\/p>\n<p>a\/c = hc\/ha<\/p>\n<p>b\/c = hc\/hb<\/p>\n<p>Since we know ha, hb, and hc (the altitudes), we will have enough information to find a, b, and c. Then we find the area by Heron\u2019s Formula.<\/p>\n<p>The formula for the area of a triangle in terms of its altitudes is:<\/p>\n<pre><code>A=1\/sqrt[(1\/ha + 1\/hb + 1\/hc)*(-1\/ha + 1\/hb + 1\/hc)*\n(1\/ha - 1\/hb + 1\/hc)*(1\/ha + 1\/hb - 1\/hc) ].<\/code><\/pre>\n<p>where  A  is the area and  ha,hb,hc  are the altitudes to sides  a,b,c , respectively.<\/p>\n<\/blockquote>\n<h3>SOLUTIONS:<\/h3>\n<p>\t\t\t\t\t\t<style>\r\n\t\t\t\t\r\n\t\t\t\t\t#tab_container_2361 {\r\n\toverflow:hidden;\r\n\tdisplay:block;\r\n\twidth:100%;\r\n\tborder:0px solid #ddd;\r\n\tmargin-bottom:30px;\r\n\t}\r\n\r\n#tab_container_2361 .tab-content{\r\n\tpadding:20px;\r\n\tborder: 1px solid #e6e6e6 !important;\r\n\tmargin-top: 0px;\r\n\tbackground-color:#ffffff !important;\r\n\tcolor: #000000 !important;\r\n\tfont-size:16px !important;\r\n\tfont-family: Open Sans !important;\r\n\t\r\n\t\tborder: 1px solid #e6e6e6 !important;\r\n\t}\r\n#tab_container_2361 .wpsm_nav-tabs {\r\n    border-bottom: 0px solid #ddd;\r\n}\r\n#tab_container_2361 .wpsm_nav-tabs > li.active > a, #tab_container_2361 .wpsm_nav-tabs > li.active > a:hover, #tab_container_2361 .wpsm_nav-tabs > li.active > a:focus {\r\n\tcolor: #000000 !important;\r\n\tcursor: default;\r\n\tbackground-color: #ffffff !important;\r\n\tborder: 1px solid #e6e6e6 !important;\r\n}\r\n\r\n#tab_container_2361 .wpsm_nav-tabs > li > a {\r\n    margin-right: 0px !important; \r\n    line-height: 1.42857143 !important;\r\n    border: 1px solid #d5d5d5 !important;\r\n    border-radius: 0px 0px 0 0 !important; \r\n\tbackground-color: #e8e8e8 !important;\r\n\tcolor: #000000 !important;\r\n\tpadding: 15px 18px 15px 18px !important;\r\n\ttext-decoration: none !important;\r\n\tfont-size: 14px !important;\r\n\ttext-align:center !important;\r\n\tfont-family: Open Sans !important;\r\n}\r\n#tab_container_2361 .wpsm_nav-tabs > li > a:focus {\r\noutline: 0px !important;\r\n}\r\n\r\n#tab_container_2361 .wpsm_nav-tabs > li > a:before {\r\n\tdisplay:none !important;\r\n}\r\n#tab_container_2361 .wpsm_nav-tabs > li > a:after {\r\n\tdisplay:none !important ;\r\n}\r\n#tab_container_2361 .wpsm_nav-tabs > li{\r\npadding:0px !important ;\r\nmargin:0px;\r\n}\r\n\r\n#tab_container_2361 .wpsm_nav-tabs > li > a:hover , #tab_container_2361 .wpsm_nav-tabs > li > a:focus {\r\n    color: #000000 !important;\r\n    background-color: #e8e8e8 !important;\r\n\tborder: 1px solid #d5d5d5 !important;\r\n\t\r\n}\r\n#tab_container_2361 .wpsm_nav-tabs > li > a .fa{\r\n\r\nmargin-right:5px !important;\r\n\r\nmargin-left:5px !important;\r\n\r\n\r\n}\r\n\r\n\t\t#tab_container_2361 .wpsm_nav-tabs a{\r\n\t\t\tbackground-image: none;\r\n\t\t\tbackground-position: 0 0;\r\n\t\t\tbackground-repeat: repeat-x;\r\n\t\t}\r\n\t\t\t\r\n\r\n\r\n#tab_container_2361 .wpsm_nav-tabs > li {\r\n    float: left;\r\n    margin-bottom: -1px !important;\r\n\tmargin-right:0px !important; \r\n}\r\n\r\n\r\n#tab_container_2361 .tab-content{\r\noverflow:hidden !important;\r\n}\r\n\r\n\r\n@media (min-width: 769px) {\r\n\r\n\t#tab_container_2361 .wpsm_nav-tabs > li{\r\n\t\tfloat:left !important ;\r\n\t\t\t\tmargin-right:-1px !important;\r\n\t\t\t\t\t}\r\n\t#tab_container_2361 .wpsm_nav-tabs{\r\n\t\tfloat:none !important;\r\n\t\tmargin:0px !important;\r\n\t}\r\n\r\n\t#tab_container_2361 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_2361 .wpsm_nav{\r\n\t\t\t}\r\n\r\n}\r\n\r\n\r\n\r\n@media (max-width: 768px) {\r\n\t#tab_container_2361 .wpsm_nav-tabs > li {\r\n\t\t\t\t\r\n\t}\r\n\t#tab_container_2361 .wpsm_nav{\r\n\t\t\t}\r\n}\r\n\r\n\r\n\t.wpsm_nav-tabs li:before{\r\n\t\tdisplay:none !important;\r\n\t}\r\n\r\n\t@media (max-width: 768px) {\r\n\t\t\t\t\r\n\t\t\t\t.wpsm_nav-tabs{\r\n\t\t\tmargin-left:0px !important;\r\n\t\t\tmargin-right:0px !important; \r\n\t\t\t\r\n\t\t}\r\n\t\t\t\t#tab_container_2361 .wpsm_nav-tabs > li{\r\n\t\t\tfloat:none !important;\r\n\t\t}\r\n\t\t\t\r\n\t}\t\t\t\t<\/style>\r\n\t\t\t\t<div id=\"tab_container_2361\" >\r\n\t \r\n\t\t\t\t\t<ul class=\"wpsm_nav wpsm_nav-tabs\" role=\"tablist\" id=\"myTab_2361\">\r\n\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t<li role=\"presentation\"  class=\"active\"  onclick=\"do_resize()\">\r\n\t\t\t\t\t\t\t\t<a href=\"#tabs_desc_2361_1\" aria-controls=\"tabs_desc_2361_1\" role=\"tab\" data-toggle=\"tab\">\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<i class=\"fa fa-code\"><\/i> \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t<span>C++<\/span>\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t<\/a>\r\n\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t<li role=\"presentation\"  onclick=\"do_resize()\">\r\n\t\t\t\t\t\t\t\t<a href=\"#tabs_desc_2361_2\" aria-controls=\"tabs_desc_2361_2\" role=\"tab\" data-toggle=\"tab\">\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<i class=\"fa fa-code\"><\/i> \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t<span>Java<\/span>\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t\t\r\n\t\t\t\t\t\t\t\t<\/a>\r\n\t\t\t\t\t\t\t<\/li>\r\n\t\t\t\t\t\t\t\t\t\t\t <\/ul>\r\n\r\n\t\t\t\t\t  <!-- Tab panes -->\r\n\t\t\t\t\t  <div class=\"tab-content\" id=\"tab-content_2361\">\r\n\t\t\t\t\t\t\t\t\t\t\t\t <div role=\"tabpanel\" class=\"tab-pane  in active \" id=\"tabs_desc_2361_1\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"cpp\"} -->\r\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\r\n#include&lt;bits\/stdc++.h&gt;\r\nusing namespace std;\r\n#define ll long long int\r\n#define ld long double\r\n#define fi first\r\n#define se second\r\n#define pb push_back\r\n\/\/\/*template{{{\r\n#define sz(x) (ll)x.size()\r\n#define all(x) x.begin(),x.end()\r\n#define trav(a,x) for(auto &amp;a:x)\r\n#define fr(i,a,b)  for(ll i=a;i&lt;=b;i++)\r\n#define fr1(i,a)   for(ll i=0;i&lt;a;i++)\r\n#define frr(i,a,b) for(ll i=b;i&gt;=a;i--)\r\n#define frr1(i,a)   for(ll i=a-1;i&gt;=0;i--)\r\n#define sorta(a,n) sort(a,a+n)\r\n#define sortd(a,n) sort(a,a+n,greater&lt;ll&gt;())\r\n#define sorva(a) sort(a.begin(),a.end())\r\n#define sortvd(a) sort(a.begin(),a.end(),greater&lt;ll&gt;())\r\n#define tc(t) while(t--)\r\n#define fio ios_base::sync_with_stdio(false);cin.tie(NULL);\r\n#define debug(...) fprintf(stderr, __VA_ARGS__), fflush(stderr)\r\nusing vi= vector&lt;ll&gt;;\r\nusing vvi= vector&lt;vi&gt;;\r\nusing vb =vector&lt;bool&gt;;\r\nusing vc =vector&lt;char&gt;;\r\nusing vs =vector&lt;string&gt;;\r\nusing vld =vector&lt;ld&gt;;\r\nusing pii =pair&lt;ll,ll&gt;;\r\nusing psi =pair&lt;string,ll&gt;;\r\nusing pci =pair&lt;char,ll&gt;;\r\nusing vpii =vector&lt;pii&gt;;\r\n\/\/}}}template*\/\r\nll const mod=998244353;\r\nll const maxn=1e5+5;\r\nll const inf=1e18;\r\nll add(ll a,ll b){\r\n    return ((a%mod)+(b%mod))%mod;\r\n}\r\nll mul(ll a,ll b){\r\n    return ((a%mod)*(b%mod))%mod;\r\n}\r\nll powm(ll x,ll n,ll M)\r\n{\r\n    ll result=1;\r\n    while(n&gt;0)\r\n    {\r\n        if(n % 2 ==1)\r\n            result=(result * x)%M;\r\n        x=(x*x)%M;\r\n        n=n\/2;\r\n    }\r\n    return result;\r\n}\r\nll modinverse(ll a, ll m){\r\n    return powm(a,m-2,m);\r\n}\r\nbool prime(ll x){\r\n    if(x&lt;=1)return false;\r\n    for(int i=2;i&lt;=sqrt(x);i++)if(x%i==0)return false;\r\n    return true;\r\n}\r\nll divisor(ll x){\r\n    ll cnt=0;\r\n    for(int i=1;i&lt;=sqrt(x);i++){\r\n        if(x%i==0){\r\n            if(i!=x\/i)cnt+=2;\r\n            else cnt+=1;\r\n        }\r\n    }\r\n    return cnt;\r\n}\r\nvector&lt;ll&gt; sieve(ll n) {    \r\n    bool prim[n+1];\r\n    memset(prim, true, sizeof(prim));\r\n    for (ll p=2; p*p&lt;=n; p++) {\r\n        if (prim[p] == true) {\r\n            for (int i=p*p; i&lt;=n; i += p)\r\n                prim[i] = false;\r\n        }\r\n    }\r\n    vector&lt;ll&gt;v;\r\n    for(int i=2;i&lt;=n;i++)if(prim[i])v.push_back(i);\r\n    return v;\r\n}\r\n\r\nvoid solve(){\r\n      long double ha,hb,hc;\r\n      cin&gt;&gt;ha&gt;&gt;hb&gt;&gt;hc;\r\n      if(ha&lt;=0 or hb&lt;=0 or hc&lt;=0){\r\n        cout&lt;&lt;&quot;IMPOSSIBLE&#92;n&quot;;\r\n        return ;\r\n      }\r\n      ha=1.0\/ha;\r\n      hb=1.0\/hb;\r\n      hc=1.0\/hc;\r\n      long double a=(ha+hb+hc);\r\n      long double b=(-ha+hb+hc);\r\n      long double c=(ha-hb+hc);\r\n      long double d=(ha+hb-hc);\r\n      if(a&lt;=0 or b&lt;=0 or c&lt;=0 or d&lt;=0){\r\n        cout&lt;&lt;&quot;IMPOSSIBLE&#92;n&quot;;\r\n        return ;\r\n      }\r\n      a=1.0\/a;\r\n      b=1.0\/b;\r\n      c=1.0\/c;\r\n      d=1.0\/d;\r\n      a=sqrtl(a);\r\n      b=sqrtl(b);\r\n      c=sqrtl(c);\r\n      d=sqrtl(d);\r\n      long double ans=a*b*c*d;\r\n      cout&lt;&lt;fixed&lt;&lt;setprecision(3)&lt;&lt;ans&lt;&lt;'&#92;n';\r\n}\r\nint main(){\r\n\r\n    fio;\r\n    ll t;\r\n    t=1;\r\n    cin&gt;&gt;t;\r\n    while(t--){\r\n        solve();\r\n    }\r\n\r\n   return 0;\r\n}\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\r\n\t\t\t\t\t\t <\/div>\r\n\t\t\t\t\t\t\t\t\t\t\t\t <div role=\"tabpanel\" class=\"tab-pane \" id=\"tabs_desc_2361_2\">\r\n\t\t\t\t\t\t\t\t<!-- wp:enlighter\/codeblock {\"language\":\"Java\"} -->\r\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"Java\" data-enlighter-theme=\"\" data-enlighter-highlight=\"\" data-enlighter-linenumbers=\"\" data-enlighter-lineoffset=\"\" data-enlighter-title=\"\" data-enlighter-group=\"\">\r\n\r\nimport java.util.*;\r\n\r\nclass Heights \r\n{\r\n    static Scanner sc=new Scanner(System.in);\r\n    static long mod=998244353;\r\n    static double maxn=1e5+5;\r\n    static double inf=1e18;\r\n\r\n    long add(long a,long b)\r\n    {\r\n        return ((a%mod)+(b%mod))%mod;\r\n    }\r\n    long mul(long a,long b){\r\n        return ((a%mod)*(b%mod))%mod;\r\n    }\r\n    long powm(long x,long n,long M)\r\n    {\r\n        long result=1;\r\n        while(n&gt;0)\r\n        {\r\n            if(n % 2 ==1)\r\n                result=(result * x)%M;\r\n            x=(x*x)%M;\r\n            n=n\/2;\r\n        }\r\n        return result;\r\n    }\r\n    long modinverse(long a, long m){\r\n        return powm(a,m-2,m);\r\n    }\r\n    boolean prime(long x){\r\n        if(x&lt;=1)return false;\r\n        for(int i=2;i&lt;=Math.sqrt(x);i++)if(x%i==0)return false;\r\n        return true;\r\n    }\r\n    long divisor(long x){\r\n        long cnt=0;\r\n        for(int i=1;i&lt;=Math.sqrt(x);i++){\r\n            if(x%i==0){\r\n                if(i!=x\/i)cnt+=2;\r\n                else cnt+=1;\r\n            }\r\n        }\r\n        return cnt;\r\n    }\r\n    ArrayList&lt;Long&gt; sieve(int n) {    \r\n        boolean []prim=new boolean[n+1];\r\n        Arrays.fill(prim, true);\r\n        for (long p=2; p*p&lt;=n; p++) {\r\n            if (prim[(int) p] == true) {\r\n                for (int i=(int) (p*p); i&lt;=n; i += p)\r\n                    prim[i] = false;\r\n            }\r\n        }\r\n        ArrayList&lt;Long&gt; v=new ArrayList&lt;&gt;();\r\n        for(long i=2;i&lt;=n;i++)\r\n        {\r\n            if(prim[(int)i]==true)\r\n            {\r\n                v.add(i);\r\n            }\r\n        }\r\n        return v;\r\n    }\r\n    static void solve()\r\n    {\r\n          double ha=sc.nextDouble(),hb=sc.nextDouble(),hc=sc.nextDouble();\r\n          if(ha&lt;=0 || hb&lt;=0 || hc&lt;=0)\r\n          {\r\n            System.out.println(&quot;MPOSSIBLE&quot;);\r\n            return ;\r\n          }\r\n          ha=1.0\/ha;\r\n          hb=1.0\/hb;\r\n          hc=1.0\/hc;\r\n          double a=(ha+hb+hc);\r\n          double b=(-ha+hb+hc);\r\n          double c=(ha-hb+hc);\r\n          double d=(ha+hb-hc);\r\n          if(a&lt;=0 || b&lt;=0 || c&lt;=0 || d&lt;=0)\r\n          {\r\n            System.out.println(&quot;MPOSSIBLE&quot;);\r\n            return ;\r\n          }\r\n          a=1.0\/a;\r\n          b=1.0\/b;\r\n          c=1.0\/c;\r\n          d=1.0\/d;\r\n          a=Math.sqrt(a);\r\n          b=Math.sqrt(b);\r\n          c=Math.sqrt(c);\r\n          d=Math.sqrt(d);\r\n          double ans=a*b*c*d;\r\n          System.out.println(String.format(&quot;%.3f&quot;, ans));\r\n         \r\n    }\r\n    public static void main(String[] args) \r\n    {\r\n        long t=sc.nextLong();\r\n        while(t!=0)\r\n        {\r\n            solve();\r\n            t--;\r\n        }\r\n    }\r\n}\r\n<\/pre>\r\n<!-- \/wp:enlighter\/codeblock -->\t\t\t\t\t\t <\/div>\r\n\t\t\t\t\t\t\t\r\n\t\t\t\t\t <\/div>\r\n\t\t\t\t\t \r\n\t\t\t\t <\/div>\r\n <script>\r\n\t\tjQuery(function () {\r\n\t\t\tjQuery('#myTab_2361 a:first').tab('show')\r\n\t\t});\r\n\t\t\r\n\t\t\t\tjQuery(function(){\r\n\t\t\tvar b=\"fadeIn\";\r\n\t\t\tvar c;\r\n\t\t\tvar a;\r\n\t\t\td(jQuery(\"#myTab_2361 a\"),jQuery(\"#tab-content_2361\"));function d(e,f,g){\r\n\t\t\t\te.click(function(i){\r\n\t\t\t\t\ti.preventDefault();\r\n\t\t\t\t\tjQuery(this).tab(\"show\");\r\n\t\t\t\t\tvar h=jQuery(this).data(\"easein\");\r\n\t\t\t\t\tif(c){c.removeClass(a);}\r\n\t\t\t\t\tif(h){f.find(\"div.active\").addClass(\"animated \"+h);a=h;}\r\n\t\t\t\t\telse{if(g){f.find(\"div.active\").addClass(\"animated \"+g);a=g;}else{f.find(\"div.active\").addClass(\"animated \"+b);a=b;}}c=f.find(\"div.active\");\r\n\t\t\t\t});\r\n\t\t\t}\r\n\t\t});\r\n\t\t\r\n\r\n\t\tfunction do_resize(){\r\n\r\n\t\t\tvar width=jQuery( '.tab-content .tab-pane iframe' ).width();\r\n\t\t\tvar height=jQuery( '.tab-content .tab-pane iframe' ).height();\r\n\r\n\t\t\tvar toggleSize = true;\r\n\t\t\tjQuery('iframe').animate({\r\n\t\t\t    width: toggleSize ? width : 640,\r\n\t\t\t    height: toggleSize ? height : 360\r\n\t\t\t  }, 250);\r\n\r\n\t\t\t  toggleSize = !toggleSize;\r\n\t\t}\r\n\r\n\r\n\t<\/script>\r\n\t\t\t\t\r\n\t\t\t<br \/>\n[forminator_quiz id=&quot;2362&quot;]<\/p>\n<p>This article tried to discuss <strong>Computational geometry<\/strong>. Hope this blog helps you understand and solve the problem. To practice more problems on Computational geometry you can check out <a href=\"#\"><\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>CONCEPTS USED: Computational geometry. DIFFICULTY LEVEL: Medium. PROBLEM STATEMENT(SIMPLIFIED): For any triangle ABC we know that the height from A to the line BC(or it&#8217;s extension) is Ha, from B to the line AC (or it&#8217;s extension) is Hb and from C to the line AB (or it&#8217;s extension) is Hc. 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