The height drawn to the base of the isosceles triangle is 10, and the height drawn to the lateral

| May 3, 2021 | education

The height drawn to the base of the isosceles triangle is 10, and the height drawn to the lateral side is 12. Find the radius of the circle inscribed in the triangle.

In an isosceles triangle, the height is both the bisector, and the median, and the height. Consequently, she divides the side by sex. Let the triangle ABC, AX-height, and AC = AB. Then XB = 16/2 = 8 cm.

By the Pythagorean theorem, we find the lateral sides:

AB = √ (AX² + XB²) = √ (6² + 8²) = √ (100) = 10 centimeters – AC and AB

Inscribed circle radius: r = S \ p.

Find the radius of the inscribed circle:

p = (10 + 10 + 16) / 2 = 18 centimeters.

S = 1 \ 2 * CB * AD = 1 \ 2 * 16 * 6 = 48 square centimeters.

r = 48 \ 18 = 2.6 centimeters.

Answer: The radius of a circle inscribed in a triangle is 2.6 centimeters.



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