MathDB

A=120, find value of PIQ

Source: Sharygin Finals 2023 9.8

August 2, 2023

geometrySharygin Geometry OlympiadSharygin 2023Angle Chasing

Problem Statement

Let

ABC

be a triangle with

\angle A = 120^\circ

,

A

be the incenter, and

E

be the midpoint of

BC

. The line passing through

E

and parallel to

FI

meets the circle with diameter

AB

at points

E

and

F

(

A

and

E

lie on the same semiplane with respect to

BC

). The line passing through

E

and perpendicular to

FI

meets

AB

and

AC

at points

P

and

Q

respectively. Find the value of

\angle PIQ

.

Back to Problems View on AoPS