In the quadrilateral ABCD the circle AB = 5, 2CD = AB is inscribed. Find the perimeter of the quadrilateral ABCD

It is known that it is possible to inscribe a circle into a quadrilateral only if the sums of its opposite sides are equal.

We have AB and DC – opposite sides.

2CD = AB;

CD = 0.5AB;

AB + DC = AB + 0.5AB = 1.5AB.

The sum of the other two sides must also equal 1.5AB.

Perimeter p = 1.5AB + 1.5AB = 3 * AB = 3 * 5 = 15.

Answer: 15.