MathDB

invert your expectations pt.2

Source: 2023 HMIC 3

April 25, 2023

InversiongeometryHMIC

Problem Statement

Triangle

ABC

has incircle

\omega

and

A

-excircle

\omega_A.

Circle

\gamma_B

passes through

B

and is externally tangent to

\omega

and

\omega_A.

Circle

\gamma_C

passes through

C

and is externally tangent to

\omega

and

\omega_A.

If

\gamma_B

intersects line

BC

again at

D,

and

\gamma_C

intersects line

BC

again at

E,

prove that

BD=EC.

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