Trapezoid ABCD is inscribed in a circle; angle A = 60 degrees; angle ABD = 90 degrees

| August 20, 2021 | education

Trapezoid ABCD is inscribed in a circle; angle A = 60 degrees; angle ABD = 90 degrees; СD = 4cm. Find the radius of the circle.

Since the trapezoid is inscribed in a circle, it is isosceles, and therefore AB = CD = 4 cm.

By condition, the angle AED = 90, then it rests on the diameter of the circle, and therefore, the base of the trapezoid is the diameter of the circle, and its center is the middle of the base.

By condition, the angle BAD = 60, then the angle ADB = 180 – ABD – BAD = 180 – 90 – 60 = 30.

In a right-angled triangle ABD, leg AB lies opposite angle 30, which means that its length is equal to half the length of the hypotenuse AD.

AB = AD / 2.

AD = 2 * AB = 2 * 4 = 8 cm.

Then the radius of the circle is: R = ОА = АD / 2 = 8/2 = 4 cm.

Answer: The radius of the circle is 4 cm.



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