A circle is inscribed in an isosceles trapezoid. The perimeter of the trapezoid is 56 cm.

| January 24, 2021 | education

A circle is inscribed in an isosceles trapezoid. The perimeter of the trapezoid is 56 cm. The tangency point divides the lateral side into segments, one of which is 5 cm. Find the base of the trapezoid.

From the center O of the circle, draw the radii to the points of tangency of the circle and the sides of the trapezoid.

By condition, ВK = СР = 5 cm.

By the property of tangents drawn to a circle from one point, the lengths of these tangents are equal. Then ВK = ВM = CM = CP = 5 cm.

BC = BM + CM = 5 + 5 = 10 cm.

Also by the property of tangents, AK = AH = DР = DН.

Let AK = AH = AR = DН = X cm.

The perimeter of the trapezoid is: Ravsd = AK = AH = DR = DН + ВK + BC + СР = 20 + 4 * X.

4 * X = 56 – 20 = 36.

X = 36/4 = 9 cm.

Then AD = 2 * X = 18 cm.

Answer: The bases of the trapezoid are 10 cm and 18 cm.



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