MathDB
Fixed point

Source: greek mo , 2005

November 12, 2005
geometrycircumcirclegeometry proposed

Problem Statement

Let OX1,OX2OX_1 , OX_2 be rays in the interior of a convex angle XOYXOY such that ∠XOX1=∠YOY1<13∠XOY\angle XOX_1=\angle YOY_1< \frac{1}{3}\angle XOY. Points KK on OX1OX_1 and LL on OY1OY_1 are fixed so that OK=OLOK=OL, and points AA, BB are vary on rays (OX,(OY(OX , (OY respectively such that the area of the pentagon OAKLBOAKLB remains constant. Prove that the circumcircle of the triangle OABOAB passes from a fixed point, other than OO.
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