An obtuse isosceles triangle is inscribed in a circle with a radius of 5 centimeters.

An obtuse isosceles triangle is inscribed in a circle with a radius of 5 centimeters. The height that is drawn to the base of this triangle is exactly 2 centimeters. Find the sides of the triangle.

The area of a triangle inscribed in a circle can be determined by the formula:

Saws = AB * BC * AC / 4 * R.

Also, the area of the triangle is:

S = AC * BH / 2.

Then: AB * BC * AC / 4 * R = AC * BH / 2.

AB * BC / 4 * 5 = 2/2.

Since AB = BC, AB2 = 20.

AB = BC = √20 = 2 * √5 cm.

From the right-angled triangle ABH, by the Pythagorean theorem, we determine the leg AH.

AH ^ 2 = AB ^ 2 – BH ^ 2 = (2 * √5) ^ 2 – 22 = 20 – 4 = 16.

AH = 4 cm.

Then AC = 2 * AH = 2 * 4 = 8 cm.

Answer: The sides of the triangle are 2 * √5 cm, 2 * √5 cm, 8 cm.