Find the radius of a circle circumscribed about an isosceles trapezoid if its bases are 10 cm and 14 cm

| April 29, 2021 | education

Find the radius of a circle circumscribed about an isosceles trapezoid if its bases are 10 cm and 14 cm, and the height is 12 cm.

Trapezium ABCD is isosceles, then the height BH divides the base of AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases. AH = (AD – BC) / 2 = (14 – 10) / 2 = 2 cm.

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

AB ^ 2 = BH ^ 2 + AH ^ 2 = 144 + 4 = 148.

AB = √148 cm.

DН = АD – АН = 14 – 2 = 12 cm.

In a right-angled triangle BDH, we determine the length of the hypotenuse BD.

BD ^ 2 = BH ^ 2 + DH ^ 2 = 144 + 144 = 288.

ВD = 12 * √2 cm.

Determine the area of ​​the triangle ABD. Savd = AD * ВН / 2 = 14 * 12/2 = 84 cm2.

The radius of a circle around a trapezoid is equal to a circle around a triangle ABD. R = AB * BD * AD / 4 * Savd = √148 * 12 * √2 * 14/4 * 84 = 8.6 cm.

Answer: The radius of the circle is 8.6 cm.



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