The hypotenuse of an isosceles triangle ABC is 20 cm Find: – the distance from the middle of the hypotenuse

The hypotenuse of an isosceles triangle ABC is 20 cm Find: – the distance from the middle of the hypotenuse to each vertex of the triangle ABC. – what property does point O have – the middle of the hypotenuse?

Let point K be the middle of the hypotenuse BC, then BK = CK = 20/2 = 10 cm.

Since the triangle ABC is isosceles, the angle ABC = ACB = 450.

KH is perpendicular to AB, then the angle BKH = BCA as the corresponding angles at the intersection of parallel KH and BC secant BC. Angle BKH = 450.

In a right-angled triangle BHK Cos45 = KH / BK.

KH = BK * Cos45 = 10 * √2 / 2 = 5 * √2 cm.

Triangles BHK and CMK are equal in hypotenuse and acute angle, then KM = KH = 5 * √2 cm.

Point K, the middle of the hypotenuse, is the center of the circle described around the triangle ABC.

Answer: The distance from the middle of the hypotenuse to the legs of the triangle is 5 * √2 cm.