MathDB
angle problem

Source: Taiwan 1st TST 2005, final exam, first day, problem 2

August 12, 2005
trigonometrygeometryincentersymmetrycyclic quadrilateralgeometry proposed

Problem Statement

PP is a point in the interior of △ABC\triangle ABC, and ∠ABP=∠PCB=10∘\angle ABP = \angle PCB = 10^\circ. (a) If ∠PBC=10∘\angle PBC = 10^\circ and ∠ACP=20∘\angle ACP = 20^\circ, what is the value of ∠BAP\angle BAP? (b) If ∠PBC=20∘\angle PBC = 20^\circ and ∠ACP=10∘\angle ACP = 10^\circ, what is the value of ∠BAP\angle BAP?
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