IMO 1969 LL FRA21

A right-angled triangle OAB has its right angle at the point B.

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IMO 1969 LL FRA21

Origin: FRA

Problem

A right-angled triangle OAB has its right angle at the point B. An arbitrary circle with center on the line OB is tangent to the line OA. Let AT be the tangent to the circle different from OA (T is the point of tangency). Prove that the median from B of the triangle OAB intersects AT at a point M such that MB = MT .