A circle is inscribed in the ABCD quadrangle. The AB side is 3 times the size of the CD side.

A circle is inscribed in the ABCD quadrangle. The AB side is 3 times the size of the CD side. Find sides AB and CD, if BC = 13 cm, AD = 15 cm.

So that a circle can be inscribed into a quadrilateral, the sums of its opposite sides must be equal, that is, for the quadrilateral ABCD, the equality must be fulfilled:
AB + CD = BC + AD.
Let CD = x, then AB = 3x (since by condition AB is 3 times more than the CD side). Then:
3x + x = 13 + 15;
4x = 28;
x = 28/4;
x = 7 cm.
CD = x = 7 cm, AB = 3x = 3 * 7 = 21 (cm).
Otw: AB = 21 cm, CD = 7 cm.