# In an isosceles triangle, the side is 15 and the base is 18. Find the radius.

September 15, 2021 | education

| Let us define the area of the triangle ABC by Heron’s theorem.

The half-perimeter of the triangle is: p = (15 + 15 + 18) / 2 = 24 cm.

Then Sav = √24 * (24 – 15) * (24 – 15) * (24 – 18) = √24 * 9 * 9 * 6 = √11664 = 108 cm2.

Determine the radius of the circumscribed circle.

R = АС * ВС * АС / 4 * Saс = 18 * 15 * 15/4 * 108 = 9.375 cm.

Determine the radius of the inscribed circle.

r = S / p = 108/24 = 4.5 cm.

Answer: The radii of the circles are 4.5 cm and 9.375 cm.

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