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Diameter of Circumcircle

Source: 1992 IrMO Paper 1 Problem 4

October 2, 2017
geometrycircumcircle

Problem Statement

In a triangle ABCABC, the points A’A’, B’B’ and C’C’ on the sides opposite AA ,BB and CC, respectively, are such that the lines AA’AA’, BB’BB’ and CC’CC’ are concurrent. Prove that the diameter of the circumscribed circle of the triangle ABCABC equals the product ∣AB’∣⋅∣BC’∣⋅∣CA’∣|AB’|\cdot |BC’|\cdot |CA’| divided by the area of the triangle A’B’C’A’B’C’.
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