Problem

Let ABC be an acute-angled triangle, let D, F be the mid-points of BC, AB respectively. Let the perpendicular from F to AC and the perpendicular at B to BC meet in N. Prove that ND is equal to circum-radius of ABC.
The discussion uses the following Theorems: Midpoint Theorem: The line segment joining midpoint of two sides of a triangle is half of and parallel to the third side. Cyclic Quadrilateral: Opposite angles of a quadrilateral add up to \( 180^o\)

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