A circle is inscribed in a rectangular trapezoid. The length of the lateral side of the trapezoid is 26

univerkov | April 25, 2021 | education

A circle is inscribed in a rectangular trapezoid. The length of the lateral side of the trapezoid is 26, and the acute angle adjacent to it is 30 degrees. Find the length of the midline of the trapezoid.

Let’s draw from the top С the height СН. In the formed right-angled triangle СDН, we determine the length of the side СН.

SinСДН = СН / СD, then СН = Sin30 * 26 = 1/2 * 26 = 13 cm.

Lateral side AB = CH = 13 cm.

Since a circle is inscribed in the trapezoid, BC + AD = AB + CD = 13 + 26 = 39 cm.

The length of the middle line of the trapezoid is: KM = (BC + AD) / 2, then KM = (AD + CD) / 2 = 39/2 = 19.5 cm.

Answer: The length of the middle line is 19.5 cm.

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