A circle is inscribed in an isosceles trapezoid with bases 9 and 16. Find its length.

Let’s build the height of the HB trapezoid.

By the property of an isosceles trapezoid, the length of the segment AH is equal to: AH = (AD – BC) / 2 = (16 – 9) / 2 = 3.5 cm.

Since a circle is inscribed in the trapezoid, then (BC + AD) = (AB + CD) = (16 + 9) = 25 cm.

And since AB = CD, then AB = CD = 25/2 = 12.5 cm.

In a right-angled triangle ABН, BH ^ 2 = AB ^ 2 – AH ^ 2 = 156.25 – 12.25 = 144.

BH = 12 cm.

The height of the trapezoid is equal to the diameter of the circle.

Then the circumference is equal to: L = π * BH = π * 12 cm.

Answer: The circumference is π * 12 cm.