MathDB

In a scalene triangle

ABC

with incenter

I

, the incircle is tangent to sides

CA

and

AB

at points

E

and

F

. The tangents to the circumcircle of triangle

AEF

E

and

F

meet at

S

. Lines

EF

and

BC

intersect at

T

. Prove that the circle with diameter

ST

is orthogonal to the nine-point circle of triangle

BIC

.
Proposed by Evan Chen

Problem Statement