MathDB

9

Part of 1987 AIME Problems

Problems(1)

Equal angles in a right triangle

Source:

3/16/2006
Triangle ABCABC has right angle at BB, and contains a point PP for which PA=10PA = 10, PB=6PB = 6, and ∠APB=∠BPC=∠CPA\angle APB = \angle BPC = \angle CPA. Find PCPC.
[asy] pair A=(0,5), B=origin, C=(12,0), D=rotate(-60)*C, F=rotate(60)*A, P=intersectionpoint(A--D, C--F); draw(A--P--B--A--C--B^^C--P); dot(A^^B^^C^^P); pair point=P; label("AA", A, dir(point--A)); label("BB", B, dir(point--B)); label("CC", C, dir(point--C)); label("PP", P, NE);[/asy]
rotationtrigonometrytrig identitiesLaw of Cosines