A quadrilateral ABCD circumscribes a circle and AB 6 cm CD 5 cm and AD 7 cm The length of side BC is...........

Quantitative Aptitude ( CCS) Geometry

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A quadrilateral ABCD circumscribes a circle and AB = 6 cm, CD = 5 cm and AD = 7 cm. The length of side BC is

4 cm

5 cm

3 cm

6 cm

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Explanation:

We know tangents drawn to a circle from same external point are equal
AM = AQ = x (let)
∴ MB = 6 – x = BN
QD = 7 – x = DP
PC = y (let) = CN
Now, CD = DP + PC = 5
⇒ 7 – x + y = 5
⇒ y – x = – 2
BC = CN + BN
= y + 6 – x = y – x + 6 = – 2 + 6 = 4