MathDB

force overlay inversion vibes

Source: USAMO 2023/6

March 23, 2023

USAMOgeometryHi

Problem Statement

Let

ABC

be a triangle with incenter

I

and excenters

I_a

,

I_b

, and

I_c

opposite

A

,

B

, and

C

, respectively. Let

D

be an arbitrary point on the circumcircle of

\triangle{ABC}

that does not lie on any of the lines

II_a

,

I_bI_c

, or

BC

. Suppose the circumcircles of

\triangle{DII_a}

and

\triangle{DI_bI_c}

intersect at two distinct points

D

and

F

. If

E

is the intersection of lines

DF

and

BC

, prove that

\angle{BAD} = \angle{EAC}

.
Proposed by Zach Chroman

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