MathDB

Let

ABC

be a triangle with

\angle ABC

obtuse. The

A

-excircle is a circle in the exterior of

\triangle ABC

that is tangent to side

BC

of the triangle and tangent to the extensions of the other two sides. Let

E

F

be the feet of the altitudes from

B

and

C

to lines

AC

and

AB

, respectively. Can line

EF

be tangent to the

A

-excircle?
Proposed by Ankan Bhattacharya, Zack Chroman, and Anant Mudgal

Problem Statement