MathDB
2018 JHMT Geometry #4

Source:

September 5, 2023
geometry

Problem Statement

Equilateral triangle OABOAB of side length 11 lies in the xyxy-plane (OO is the origin). Let ℓ,m\ell, m be the vertical lines passing through A,BA,B, respectively. Let P,QP,Q be on ℓ,m\ell, m respectively such that the ratio OP‾:OQ‾:PQ‾=3:3:5\overline{OP} : \overline{OQ} : \overline{PQ} = 3 : 3 : 5. Let Q=(x,y,z)Q = (x, y, z). If z2=pqz^2 = \frac{p}{q} . where p,qp, q are relatively prime positive integers, find p+qp + q.
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