MathDB

2017 PUMaC Individual Finals A3

Source:

September 19, 2019

geometry

Problem Statement

Triangle

ABC

has incenter

I

. The line through

I

perpendicular to

AI

meets the circumcircle of

ABC

at points

P

and

Q

, where

P

and

B

are on the same side of

AI

. Let

X

be the point such that

PX

//

CI

and

QX

//

BI

. Show that

P B, QC

, and

IX

intersect at a common point.

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