CMIMC 2016 Geometry Test/Problem 1

Problem
ABC is an equilateral triangle. P is a point on BC such that PB=50 and PC=30. Compute PA.

Answer
70

Solution
Let X be the midpoint of BC. By the problem conditions, we have XP=10 and BC=80. ABC is equilateral so AX = 40 \sqrt{3}. By the Pythagorean Theorem on AXP, AP=70.