A circle is inscribed in an isosceles trapezoid ABCD (BC || AD). The length of the middle line

univerkov | April 9, 2021 | education

A circle is inscribed in an isosceles trapezoid ABCD (BC || AD). The length of the middle line of this trapezoid is 6 cm. Calculate the length of the side of the trapezoid.

Since a circle is inscribed in a trapezoid, the sum of the lengths of the bases of this trapezoid is equal to the sum of the lengths of its lateral sides.

AB + CD = BC + AD.

We use the formula for the midline of the trapezoid.

KM = (BC + AD) / 2.

BC + AD = KM * 2 = 6 * 2 = 12 cm.

Then AB + CD = 12 cm.

Since, by condition, the trapezoid is isosceles, then AB = CD, then 2 * AB = 12.

AB = CD = 12/2 = 6 cm.

Answer: The length of the side is 6 cm.

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