8.3

Part of 2006 Sharygin Geometry Olympiad

Problems(1)

paralellogram and 2 circles given. equal segments wanted

Source: Sharygin 2006 finals 8.3

A parallelogram

ABCD

is given. Two circles with centers at the vertices

A

C

B

. The straight line

\ell

that passes through

B

and crosses the circles at second time at points

X, Y

respectively. Prove that

DX = DY

geometryparallelogramcirclesequal segments