The height drawn to the base of the isosceles triangle is 9 cm, and the base itself is 24 cm

| May 1, 2021 | education

The height drawn to the base of the isosceles triangle is 9 cm, and the base itself is 24 cm. Find the radii of the inscribed in the triangle and circumscribed about the triangles of circles.

We will draw from the top B to the height of the ВН, to the base of the AC.

Since, by condition, the triangle is isosceles, then its height BH is the median of the triangle and divides its base AC in half, AH = CH = AC / 2 = 24/2 = 12 cm.

In a right-angled triangle ABН, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

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

AB = 15 cm.

Determine the area of ​​the triangle ABC.

Savs = AC * ВН / 2 = 24 * 9/2 = 108 cm.

Let’s define the semiperimeter of the triangle ABC.

p = (AB + BC + AC) / 2 = (15 + 15 + 24) / 2 = 27 cm.

Determine the radius of the inscribed circle.

r = S / p = 108/27 = 4 cm.

Determine the radius of the circumscribed circle.

R = (AB * BC * AC) / S * 4 = (15 * 15 * 24) / 108 * 4 = 5400/432 = 12.5 cm

Answer: The radius of the inscribed circle is 4 cm, the radius of the inscribed circle is 12.5 cm.



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