# Find the radius of a circle around an isosceles triangle if the base is 12cm and the height drawn to the base is 18cm.

August 30, 2021 | education

| The height drawn to the base of an isosceles triangle is perpendicular to it and divides it in half. This means that the height, half of the base and the side form a right-angled triangle, in which the side side is the hypotenuse. Find the square of the side by the Pythagorean theorem:

a ^ 2 = 18 ^ 2 + 6 ^ 2 = 324 + 36 = 360;

a = √360 = 6√10 cm – side.

The area of this triangle is equal to half the product of the base and the height:

S = 0.5 * 12 * 18 = 108 cm2.

The radius of a circle circumscribed about a triangle is determined by the formula:

R = abc / 4S, where a, b, c are the lengths of the sides of the triangle, S is its area.

R = 12 * 6√10 * 6√10 / (4 * 108) = 4320/432 = 10 cm.

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