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Segment equal to circumradius

Source: (Indian) RMO 2008 Problem 1

November 9, 2008
geometrycircumcirclegeometric transformationreflectionrectangletrigonometrygeometry unsolved

Problem Statement

Let ABC ABC be an acute angled triangle; let D,F D,F be the midpoints of BC,AB BC,AB respectively. Let the perpendicular from F F to AC AC and the perpendicular from B B ti BC BC meet in N N: Prove that ND ND is the circumradius of ABC ABC. [15 points out of 100 for the 6 problems]
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