A circle is described around the isosceles trapezoid ADCD. “Angle A” = 60 °.

| May 11, 2021 | education

A circle is described around the isosceles trapezoid ADCD. “Angle A” = 60 °. “Angle ABD” = 90 °. CD = 4 cm. Find the radius of the circumscribed circle (R).

According to the condition, the angle ABD = 90, since a circle is described around the trapezoid, and the internal angle is 90, this angle is based on the diameter of the circle, therefore, the base AD passes through the center of the circle and is its diameter.

In a right-angled triangle ABD, by condition, the angle BAD = 60, then the angle ADB = 180 – 90 – 60 = 30. The leg AB lies opposite the angle 30, and is equal to half the length of the hypotenuse AD. AD = 2 * AB.

Since the trapezoid is isosceles, AB = CD = 4 cm. AD ​​= 2 * 4 = 8 cm.

Then the radius of the circumscribed circle is: R = OA = AB / 2 = 8/2 = 4 cm.

Answer: The radius of the circumscribed circle is 4 cm.



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