MathDB

SMT 2023 Geometry #6

Source:

August 9, 2023

geometry

Problem Statement

Let ABC be a triangle and

\omega_1

its incircle. Let points

D

and

E

be on segments

AB

,

AC

respectively such that

DE

is parallel to

BC

and tangent to

\omega_1

. Now let

\omega_2

be the incircle of

\vartriangle ADE

and let points

F

and

G

be on segments

AD,

AE

respectively such that F G is parallel to

DE

and tangent to

\omega_2

. Given that

\omega_2

is tangent to line

AF

at point X and line

AG

at point

Y

, the radius of

\omega_1

is

60

, and

4(AX) = 5(F G) = 4(AY),

compute the radius of

\omega_2

.

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