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7

Part of 2001 239 Open Mathematical Olympiad

Problems(1)

OE + OF <= 2 (R_1 + R_2), externally tangent circles inside ABCD

Source: 239 MO 2001 X-XI p7

5/7/2020
The quadrangle ABCD ABCD contains two circles of radii R1 R_1 and R2 R_2 tangent externally. The first circle touches the sides of DA DA ,AB AB and BC BC , moreover, the sides of AB AB at the point E E . The second circle touches sides BC BC , CD CD and DA DA , and sides CD CD at F F . Diagonals of the quadrangle intersect at O O . Prove that OE+OF≤2(R1+R2) OE + OF \leq 2 (R_1 + R_2) .
(F. Bakharev, S. Berlov)
geometric inequalitytangent circlescirclesgeometryradii