In an isosceles trapezoid, the lengths of the bases of which are 21 and 9, the height is 8.

| September 19, 2021 | education

In an isosceles trapezoid, the lengths of the bases of which are 21 and 9, the height is 8. find the radius of the circumscribed circle.

Since the trapezoid is inscribed in a circle, this trapezoid is isosceles.

Then the height BH cuts off on the basis of AD giving a segment, the largest of which is equal to the half-sum of the bases, and the smaller segment is equal to the half-difference of the bases.

DH = (AD + BC) / 2 = 30/2 = 15 cm.

AH = (AD – BC) / 2 = 12/2 = 6 cm

From the right-angled triangle ВDН we determine the length of the hypotenuse ВD.

BD ^ 2 = DH ^ 2 + BH ^ 2 = 15 ^ 2 + 8 ^ 2 = 225 + 64 = 289.

ВD = 17 cm.

From the right-angled triangle ABN, we determine the length of the hypotenuse AB.

AB ^ 2 = BH ^ 2 + AH ^ 2 = 8 ^ 2 + 6 ^ 2 = 64 + 36 = 100.

AB = 10 cm.

Determine the area of ​​the triangle ABD.

Savd = АD * BН / 2 = 21 * 8/2 = 84 cm2.

Let’s define the radius of the circle through the triangle ABD inscribed in it.

R = (AB * BD * AD) / 4 * Savd = 10 * 17 * 21/4 * 84 = 3570/336 = 85/8 = 10.625 cm.

Answer: The radius of the circle is 10.625 cm.



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