Question

In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 5 cm, BC = 7 cm adn CS = 3 cm. Then, the length AB = ?

(a) 9 cm (b) 10 cm (c) 12 cm (d) 8 cm

Answer 1

AP = 5 cm
BC = 7cm
CS = 3 cm

AQ = AP = 5 cm [Length of a tangent from an external point to a circle are equal.] .....(1)
RC = CS = 3 cm [Length of a tangent from an external point to a circle are equal.]
BR = BC - RC = 4 cm
QB = BR = 4 cm [Length of a tangent from an external point to a circle are equal.] .....(2)
Therefore, from (1) and (2)

AB= AQ+QB= 5 cm + 4 cm = 9 cm