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Chisinau MO p29 1949-56 VIII-IX products from a point on circumcircle

Source:

March 15, 2021
geometryProductcircumcircle

Problem Statement

Let MM be an arbitrary point of a circle circumscribed around an acute-angled triangle ABCABC. Prove that the product of the distances from the point MM to the sides ACAC and BCBC is equal to the product of the distances from MM to the side ABAB and to the tangent to the circumscribed circle at point CC.
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