The quadrilateral ABCD is circumscribed about a circle find the sides BC and AD if AB = 7 cm

univerkov | January 8, 2021 | education

The quadrilateral ABCD is circumscribed about a circle find the sides BC and AD if AB = 7 cm CD = 11 cm BC is 2 times less than AD.

By the property of a quadrilateral circumscribed about a circle, the sum of the lengths of its opposite sides is equal to. (AB + CD) = (AD + BC).
Let the length of the BC side be equal to X cm, then, by condition, the length of the AD side is 2 * X cm.
Then (7 + 11) = (X + 2 * X).
3 * X = 18.
X = 18/3 = 6.
BC = 6 cm.
AD= 2 * 6 = 12 cm.
Answer: The length of the BC side is 6 cm, the AD is 12 cm.

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