MathDB

Geometry - simple

Source: 0

October 4, 2005

geometrygeometric transformationpower of a point

Problem Statement

Two circles

C_1

and

C_2

intersect at two distinct points

P, Q

in a plane. Let a line passing through

AB

meet the circles

C_1

and

C_2

in

A

and

B

respectively. Let

Y

be the midpoint of

AB

and let

QY

meet the cirlces

C_1

and

C_2

in

X

and

Z

respectively. Show that

Y

is also the midpoint of

XZ

.

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