Quadrilateral ABCD is circumscribed about a circle. Find sides AB and CD if BC = 6 cm, AD = 9 cm
| July 28, 2021 | education
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.
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