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Center on line IG

Source: Philippine MO 2022/4

March 18, 2022

geometryincenterexterior angleangle bisector

Problem Statement

Let

\triangle ABC

have incenter

I

and centroid

G

. Suppose that

P_A

is the foot of the perpendicular from

C

to the exterior angle bisector of

B

, and

Q_A

is the foot of the perpendicular from

B

to the exterior angle bisector of

C

. Define

P_B

,

P_C

,

Q_B

, and

Q_C

similarly. Show that

P_A, P_B, P_C, Q_A, Q_B,

and

Q_C

lie on a circle whose center is on line

IG

.

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