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Point P is chosen at random inside a square ABCD. What is the probability that triangle ABP has a greater area than each of triangles BCP and CDP?

 May 22, 2020
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 P cannot fall into area ABFE, because then, any triangle DPC is greater than any triangle APB.  P also cannot fall into area EID because all triangles BPC would be greater than all triangles APB.

If P falls into any of the regions IFC, ICG of IGD, all triangles APB will have greater areas than either triangles BPC or CPD. And these areas are 3/8 of the square ABCD = 37.5%.....so that's the probabilty that triangle APB will have a greater area than either BPC or CPD.

Hope this helps, whymenotsmart^m^.

 
 May 22, 2020
edited by whymenotsmart  May 22, 2020
edited by whymenotsmart  May 22, 2020

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