MathDB

Midpoint of AB is also the midpoint of YZ

Source: Baltic Way 1997

January 28, 2011

geometryparallelogramgeometry proposed

Problem Statement

Two circles

\mathcal{C}_1

and

\mathcal{C}_2

intersect in

P

and

Q

. A line through

P

intersects

\mathcal{C}_1

and

\mathcal{C}_2

again at

A

and

B

, respectively, and

X

is the midpoint of

AB

. The line through

Q

and

X

intersects

C_1

and

C_2

again at

Y

and

Z

, respectively. Prove that

X

is the midpoint of

YZ

.

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