MathDB

Simple angle chase

Source: PErA 2024/4

March 4, 2024

geometry

Problem Statement

Let

ABC

be a triangle, and let

E

,

F

be the feet of the altitudes from

B

and

C

to sides

AC

and

AB

, respectively. Let

P

and

Q

be the intersections of

EF

with the tangents from

B

and

C

to

(ABC)

, respectively. If

M

is the midpoint of

BC

, prove that

(PQM)

is tangent to

BC

at

M

.

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