# 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 \( 180^o\)#### Math Olympiad Program

Cheenta Math Olympiad program is designed for outstanding school students. Learn More

#### Learning Portal

Math Olympiad Portal has more problems and learning tools. Learn More