The base of an isosceles triangle is 18 cm, and the lateral side is 15 cm. Find the radii of the circles inscribed

| January 6, 2021 | education

The base of an isosceles triangle is 18 cm, and the lateral side is 15 cm. Find the radii of the circles inscribed in the triangle and circumscribed about the triangle?

We will construct the height of the ВН of an isosceles triangle. ВН is also the median of the triangle ABC, then AH = CH = AC / 2 = 18/2 = 9 cm.
By the Pythagorean theorem, BH2 = AB2 – AH2 = 225 – 81 = 144.
BH = 12 cm.
Let’s define the area of the triangle ABC. Savs = AC * ВН / 2 = 18 * 12/2 = 108 cm2.
Determine the perimeter of the triangle Ravs = 18 + 15 + 15 = 48 cm, then p = P / 2 = 24 cm.
Determine the radius of the inscribed circle. R1 = Savs / p = 108/24 = 4.5 cm.
Determine the radius of the circumscribed circle. R2 = AB * BC * AC / 4 * Saabs = 18 * 15 * 15/4 * 108 = 15 * 15/2 * 12 = 225/24 = 9 (9/24) = 9.375 cm.
Answer: The radii of the circles are 4.5 cm 9.375 cm.



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