An isosceles trapezoid is described around the circle, the angle at the base of which is 30 degrees.

univerkov | January 3, 2021 | education

An isosceles trapezoid is described around the circle, the angle at the base of which is 30 degrees. The height of the trapezoid is 4 cm. Find the sum of the lengths of the bases of the trapezoid.

In a right-angled triangle СНD, the CH leg is located opposite an angle of 300, then its length is equal to half the length of the hypotenuse of the СD.
CH = СD / 2. СD = 2 * CH = 2 * 4 = 8 cm.
Since the trapezoid is isosceles, then AB = СD = 8 cm, and the sum of the sides will be equal to: AB + СD = 8 + 8 = 16 cm.
A circle can be inscribed into a trapezoid only when the sum of its opposite sides is equal to each other. Then BC + AD = AB + СD = 16 cm.
Answer: The sum of the lengths of the bases of the trapezoid is 16 cm.

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