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There exists a not necessarily convex quadrilateral ABCD such that ∠B = ∠C = 60◦ and ∠A = 30◦ . Lines AB and CD intersect at E, lines AD and BC intersect at F, and EF meets BD at P. If CF = AE = 1, then EP2 can be expressed as m n where m and n are relatively prime positive integers. Find the value of m + n

 Jul 12, 2023
 #1
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Hi! 

 

I was just wondering if you were given a graph. If so could you possibly send it?smiley

 Jul 12, 2023
 #2
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no i was not given a graph. i was wondering if anyone has any idea how to draw one

Guest Jul 12, 2023
 #3
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Hi! 

 

Replying back: By golly did this take long, here is your graph that I think is correct for the problem. Now the main key for making a sketch like that is to think about a concave quadrilateral. Especially about the common ones. Then after you have found it makes adjustments to your graph to make it follow the requirements. Hope you can do it from here smiley!

 

IN THIS GRAPH G = P IN YOUR PROBLEM

 Jul 12, 2023

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