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9.7

Part of V Soros Olympiad 1998 - 99 (Russia)

Problems(2)

cut 10x20 rectangle in 2 pieces I (V Soros Olympiad 1998-99 Round 1 9.7)

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5/25/2024
Cut the 1010 cm ×20\times 20 cm rectangle into two pieces with one straight cut so that they can fit inside the 19.519.5 cm diameter circle without intersecting.
geometryrectangle
arc midpoint equidistant from incenters (V Soros Olympiad 1998-99 Round 3 9.7)

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5/25/2024
Consider the cyclic quadrilateral ABCDABCD. Let MM be the point of intersection of its diagonals, and LL be the midpoint of the arc ADAD (not containing other vertices of the quadrilateral). Prove that the distances from LL to the centers of the circles inscribed in triangles ABMABM and CDMCDM are equal.
geometryincenter