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Mn=ae+af

Source: 17-th Iranian Mathematical Olympiad 1999/2000

December 14, 2005
geometryrectangletrapezoidgeometry proposed

Problem Statement

Circles C1 C_1 and C2 C_2 with centers at O1 O_1 and O2 O_2 respectively meet at points A A and B B. The radii O1B O_1B and O2B O_2B meet C1 C_1 and C2 C_2 at F F andE E. The line through B B parallel to EF EF intersects C1 C_1 again at M M and C2 C_2 again at N N. Prove that MN \equal{} AE \plus{} AF.
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