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Spot the symmetry

Source: BdMO 2024 Higher Secondary National P5

March 18, 2024

geometryincirclehomothetyAngle Chasingexcircle

Problem Statement

Let

I

be the incenter of

\triangle ABC

and

P

be a point such that

PI

is perpendicular to

BC

and

PA

is parallel to

BC

. Let the line parallel to

BC

, which is tangent to the incircle of

\triangle ABC

, intersect

AB

and

AC

at points

Q

and

R

respectively. Prove that

\angle BPQ = \angle CPR

.

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