MathDB

Three fixed circles pass through the points

A

and

B

. Let

X

be a variable point on the first circle different from

A

and

B

. The line

AX

intersects the other two circles at

Y

and

Z

(with

Y

between

X

and

Z

). Show that the ratio

\frac{XY}{YZ}

is independent of the position of

X

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