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<PXY=90^o wanted, <CPA=90^o, <CBP=<CAP, midpoints (2018 NZOMC Camp Sel. p4)

Source:

January 10, 2021

geometryright angleequal angles

Problem Statement

Let

P

be a point inside triangle

ABC

such that

\angle CPA = 90^o

and

\angle CBP = \angle CAP

. Prove that

\angle P XY = 90^o

, where

X

and

Y

are the midpoints of

AB

and

AC

respectively.