A circle is inscribed in an isosceles trapezoid ABCD. Find its radius if it is known that AB = 8
| July 9, 2021 | education
A circle is inscribed in an isosceles trapezoid ABCD. Find its radius if it is known that AB = 8, and the angle ABC is equal to 150 degrees.
Let us omit the height BH of the trapezoid. In a right-angled triangle ABН, the angle ABН = ABC – СBН = 150 – 90 = 60, then the angle BAН = 180 – 90 – 60 = 30.
The BH leg lies opposite an angle of 30, then its length is equal to half the length of the hypotenuse AB.
BH = AB / 2 = 8/2 = 4 cm.
The height of the trapezoid into which the circle is inscribed is equal to the diameter of this circle, then OK = BH / 2 = 4/2 = 2 cm.
Answer: The radius of the inscribed circle is 2 cm.
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