MathDB

Let a circle through

B

and

C

of a triangle

ABC

intersect

AB

and

AC

Y

and

Z

, respectively. Let

P

be the intersection of

BZ

and

CY

, and let

X

be the intersection of

AP

and

BC

. Let

M

be the point that is distinct from

X

and on the intersection of the circumcircle of the triangle

XYZ

with

BC

. Prove that

M

is the midpoint of

BC

Problem Statement