Find the radius of a circle circumscribed about an isosceles triangle with a base of 16 cm and a height of 4 cm.

| January 16, 2021 | education

First, let’s find the length of the lateral side of this isosceles triangle.
Consider one of the two identical triangles into which the height divides this triangle.
Such a triangle is right-angled, one of the legs of which is the height of the isosceles triangle, the other leg is half of the base of this isosceles triangle, and the hypotenuse is the side of the isosceles triangle.
Using the Pythagorean theorem, we find the length of the lateral side of a given isosceles triangle:
√ (4 ^ 2 + (16/2) ^ 2) = √ (4 ^ 2 + 8 ^ 2) = √ (16 + 64) = √80 = 4√5 cm.
Applying the formula for the area of ​​a triangle by the length of its side and the height lowered to this side, we find the area S of this triangle:
S = 4 * 16/2 = 4 * 8 = 32.
Applying the formula for the area of ​​a triangle in terms of the radius R of the inscribed circle, we find R:
R = 4√5 * 4√5 * 16 / (4 * 32) = 80 * 16 / (128) = 10 cm.
Answer: 10 cm.



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