Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm, then AD = ________.

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Solution

ABCD is a quadrilateral such that its sides touches the circle with centre O at P, Q, R and S.

We know that the lengths of the tangents drawn from an external point to a circle are equal. Therefore,

AR = AS .....(1)

DR = DQ .....(2)

BP = SB .....(3)

CP = CQ .....(4)

Adding (1), (2), (3) and (4), we get

AR + DR + BP + CP = AS + SB + CQ + DQ

⇒ AD + BC = AB + CD

⇒ AD + 7 cm = 6 cm + 4 cm

⇒ AD = 10 − 7 = 3 cm

Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm, then AD = 3 cm.

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Similar questions

Quadrilateral ABCD is circumscribed to a circle. If AB = 6 cm, BC = 7 cm and CD = 4 cm then the length of AD is

(a) 3 cm (b) 4 cm (c) 6 cm (d) 7 cm

A B = 6 c m, B C = 7 c m

C D = 4 c m

A B C D

A B = 4.5 c m, B C = 5.5 c m, C D = 4 c m, A D = 6 c m

A C = 7 c m

In Fig. 8.59, a circle touches all the four sides of a quadrilateral ABCD with AB =6 cm, BC =7 cm and CD =4 cm. Find AD.

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