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Six sets of all points P inside triangle ABC

Source: Canadian Repêchage 2012: Problem 4

May 19, 2014
ratiogeometryperpendicular bisectorgeometry proposed

Problem Statement

Let ABCABC be a triangle such that ∠BAC=90∘\angle BAC = 90^\circ and AB<ACAB < AC. We divide the interior of the triangle into the following six regions: \begin{align*} S_1=\text{set of all points }\mathit{P}\text{ inside }\triangle ABC\text{ such that }PA49:149 : 1. Determine the ratio AC:ABAC : AB.
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