The height drawn to the base of the isosceles triangle is 12 cm, and the base itself is 18 cm.

| September 6, 2021 | education

The height drawn to the base of the isosceles triangle is 12 cm, and the base itself is 18 cm. Find the radii of the inscribed in the triangle and circumscribed about the triangle.

Since the triangle is isosceles, the height BH divides the base of the AC into equal segments. AH = CH = AC / 2 = 18/2 = 9 cm.

From the right-angled triangle AH, by the Pythagorean theorem, we define the hypotenuse AB.

AB ^ 2 = AH ^ 2 + BH ^ 2 = 9 ^ 2 + 12 ^ 2 = 81 + 144 = 225.

AB = BC = 15 cm.

Let’s calculate the area and semiperimeter of the triangle.

Savs = AC * BH / 2 = 12 * 18/2 = 108 cm2.

p = (AB + BC + AC) / 2 = (15 + 15 + 18) / 2 = 24 cm.

Then the radius of the inscribed circle is: r = S / p = 108/24 = 4.5 cm.

Let’s calculate the radius of the circumscribed circle.

R = (AB * BC * AC) / (4 * S) = 15 * 15 * 18/4 * 108 = 75/8 = 9.375 cm.

Answer: The radius of the inscribed circle is 4.5 cm, the radius of the inscribed circle is 9.375 cm.



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