Question

15 points!!!!!!The median AM of triangle ∆ABC is half the length of the side towards which it is drawn, BC . Prove that triangle ∆ABC is a right triangle.

Answer 1

Points A, B, and C are equidistant from point M, so lie on a circle centered at M. That makes BC a diameter, and it means that inscribed angle BAC intercepts an arc of 180°.

The measure of the inscribed angle is half the measure of the arc, so ∠BAC is 90° and ΔABC is a right triangle.