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Two tangent circles and an angle bisector

Source: Lithuanian Mathematical Olympiad 2006

April 12, 2006

geometrytrapezoidangle bisectorgeometry unsolved

Problem Statement

Two circles are tangent externaly at a point

B

. A line tangent to one of the circles at a point

A

intersects the other circle at points

C

and

D

. Show that

A

is equidistant to the lines

BC

and

BD

.

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