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Problem 346. Equal circles, Tangents, Hexagon, Semiperimeter.
Level: High School, College, SAT Prep.

The figure shows equal circles A, B, and C. AA1 and CC1 are tangents to circle B, AA2 and BB1 are tangents to circle C, and BB2 and CC2 are tangents to circle A. Points D, E, F, G, H, and M are the intersection points of the tangents AA1 with BB2, AA1 with CC1, BB1 with CC1, BB1 with AA2, CC2 with AA2, and CC2 with BB2, respectively. If s is the semiperimeter of the hexagon DEFGHM, prove that s = DM+EF+GH = DE+FG+HM.

Circles, Tangents, Hexagon, Semiperimeter


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