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Problem 6

Part of 2021 Bangladesh Mathematical Olympiad

Problems(1)

Find a+b where a/b is the length QA

Source: Bangladesh Mathematical Olympiad 2021 Problem 6

2/26/2022
Let ABCABC be an acute-angled triangle. The external bisector of ∠BAC\angle BAC meets the line BCBC at point NN. Let MM be the midpoint of BCBC. PP and QQ are two points on line ANAN such that, ∠PMN=∠MQN=90∘\angle PMN=\angle MQN=90^{\circ}. If PN=5PN=5 and BC=3BC=3, then the length QAQA can be expressed as ab\frac{a}{b} where aa and bb are co-prime positive integers. What is the value of (a+b)(a+b)?
geometry