An isosceles trapezoid is described around the circle, the perimeter of which is 10 cm. Find the length of the side.

Theorem: the sums of the opposite sides of a quadrilateral circumscribed around a circle are equal. Perimeter of an equal trapezoid: a + b + c + c = P = 10. a – lower base, b – upper base, c – lateral side. By the property of the described quadrilateral: a + b = 2c Substitute in the expression for the perimeter: 10 = 2c + 2c = 4c <=> c = 2.5 cm.
Answer: The side length is 2.5 cm.