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055

Part of 1964 All Russian Mathematical Olympiad

Problems(1)

ASU 055 All Russian MO 1964 11.2 tangential trapezoid

Source:

6/18/2019
Let ABCDABCD be an tangential trapezoid, EE is a point of its diagonals intersection, r1,r2,r3,r4r_1,r_2,r_3,r_4 -- the radiuses of the circles inscribed in the triangles ABEABE, BCEBCE, CDECDE, DAEDAE respectively. Prove that 1/(r1)+1/(r3)=1/(r2)+1/(r4).1/(r_1)+1/(r_3) = 1/(r_2)+1/(r_4).
geometrytangentialtrapezoid