An isosceles triangle with a height drawn to the base is inscribed in a circle with a diameter of 10 cm.

An isosceles triangle with a height drawn to the base is inscribed in a circle with a diameter of 10 cm. Find the base of the triangle if the height is 2cm.

Let’s draw the radii of the circle OB and OC.

ОВ = OС = КМ / 2 = 10/2 = 5 cm.

Let’s draw the radius OA perpendicular to the base of the triangle ABC.

The ВOС triangle is isosceles, since OB = OC = 5 cm, and its height OH we divide the base of the BC in half as the median of the triangle DH = CH = CD / 2.

The length of the segment OH = OA – AH = 5 – 2 = 3 cm.

Then, from the right-angled triangle COН, we determine the length of the leg CH.

CH ^ 2 = OC ^ 2 – OH ^ 2 = 25 – 9 = 16.

CH = 4 cm.

Then CB = 2 * CH = 2 * 4 = 8 cm.

Answer: The length of the base of the triangle is 8 cm.