MathDB

2

Part of 2014 ITAMO

Problems(1)

H is the foot of the altitude on AB, such that AH=3HB

Source: Itamo 2014 - p2

11/19/2014
Let ABCABC be a triangle. Let HH be the foot of the altitude from CC on ABAB. Suppose that AH=3HBAH = 3HB. Suppose in addition we are given that
(a) MM is the midpoint of ABAB; (b) NN is the midpoint of ACAC; (c) PP is a point on the opposite side of BB with respect to the line ACAC such that NP=NCNP = NC and PC=CBPC = CB.
Prove that ∠APM=∠PBA\angle APM = \angle PBA.
symmetrygeometrycircumcirclegeometry unsolved