# Quadrilateral ABCD is circumscribed about a circle. Find sides AB and CD if BC = 6 cm, AD = 9 cm

Quadrilateral ABCD is circumscribed about a circle. Find sides AB and CD if BC = 6 cm, AD = 9 cm, AB is twice as large as CD.

Given: the quadrilateral ABCD is circumscribed about a circle. BC = 6 cm, AD = 9 cm, AB is twice as large as CD.

Find: AB and CD.

Solution. Property of a quadrilateral circumscribed about a circle: if a quadrilateral is circumscribed about a circle, then the sum of its two opposite sides is equal to the sum of its other two sides.

AB + DC = BC + AD.

By condition AB = 2 * DC.

2 * DC + DC = BC + AD.

3 * DC = BC + AD.

3 * DC = 6 + 9.

3 * DC = 15.

DC = 15: 3.

DC = 5 (cm).

AB = 2 * DC.

AB = 2 * 5.

AB = 10 (cm).

Answer: DC = 5 cm, AB = 10 cm. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.