In trapezoid ABCD with bases AD and BC, it is known that AD = 6, BC = AB
| August 12, 2021 | education
In trapezoid ABCD with bases AD and BC, it is known that AD = 6, BC = AB = CD = 3. Find the radius of the circle tangent to side AD and lines AB and CD.
Let’s extend the lateral sides AB and CD of the trapezoid, until they intersect at point E. The result is a circle inscribed in the triangle AED.
By condition, BC = 3 cm, AD = 6 cm, so BC is the middle line of the triangle AED, and therefore AB = BE = DC = CE = 6 cm. Then the triangle AED is equilateral.
The radius of the inscribed circle in an equilateral triangle is determined by the formula:
R = a * √3 / 6, where a is the side length of an equilateral triangle.
R = 6 * √3 / 6 = √3 cm.
Answer: The radius of the circle is √3 cm.
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