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In the diagram, square ABCD has sides of length 4, and triangle ABE is equilateral. Line segments BE and AC intersect at P. Point Q is on BC so that PQ is perpendicular to BC and PQ=x.  Compute AP.

 

 Jun 19, 2021
 #1
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PQ = CQ = x         ∠PCQ = 45º         ∠PBQ = 30º

 

tan(45º) * x = tan(30º) * (4 - x)

 

x = 2(√3 -1) ≈ 1.464

 Jun 19, 2021

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