In the given figure, quadrilateral ABCD is circumscribed. The circle touches the sides AB, BC, CD, DA at P, Q, R, S respectively. If AP = 9 cm, BP = 7 cm, CQ = 5 cm and DR = 6 cm, find the perimeter of quadrilateral ABCD.

50 cm

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54 cm

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58 cm

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62 cm

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Solution

The correct option is B 54 cm

DS = DR = 6 cm

CR = CQ = 5 cm

BQ = BP = 7 cm

AS = AP = 9 cm

Perimeter of the quadrilateral ABCD = AS + DS + DR + CR + CQ + BQ + BP + AP

= 9 cm + 6 cm + 6 cm + 5 cm + 5 cm + 7 cm + 7 cm + 9 cm

= 54 cm.

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Similar questions

In the given figure, quadrilateral ABCD is circumscribed. The circle touches the sides AB, BC, CD and DA at P, Q, R, S respectively. If AP = 9 cm, BP = 7 cm, CQ = 5 cm and DR = 6 cm, find the perimeter of quad. ABCD.

Q. In the given figure, quadrilateral ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 6 cm, BP = 5 cm, CQ = 3 cm and DR = 4 cm, then the perimeter of quadrilateral ABCD is

(a) 18 cm
(b) 27 cm
(c) 36 cm
(d) 32 cm

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

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

In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S. If AP = 16 cm, BP = 5 cm, CQ = 3 cm adn DR = 4 cm then perimeter of quad. ABCD is

(a) 18 cm (b) 27 cm (c) 36 cm (d) 32 cm

Q. In the given figure, ABCD is a quadrilateral in which ∠D = 90°. A circle C(O, r) touches the sides AB, BC, CD and DA at P, Q, R, S, respectively. If BC = 38 cm, CD = 25 cm and BP = 27 cm, find the value of r.

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In the given figure, quadrilateral ABCD is circumscribed. The circle touches the sides AB, BC, CD, DA at P, Q, R, S respectively. If AP = 9 cm, BP = 7 cm, CQ = 5 cm and DR = 6 cm, find the perimeter of quadrilateral ABCD.

The correct option is B 54 cm DS = DR = 6 cm CR = CQ = 5 cm BQ = BP = 7 cm AS = AP = 9 cm Perimeter of the quadrilateral ABCD = AS + DS + DR + CR + CQ + BQ + BP + AP = 9 cm + 6 cm + 6 cm + 5 cm + 5 cm + 7 cm + 7 cm + 9 cm = 54 cm.

The correct option is B 54 cm

DS = DR = 6 cm

CR = CQ = 5 cm

BQ = BP = 7 cm

AS = AP = 9 cm

Perimeter of the quadrilateral ABCD = AS + DS + DR + CR + CQ + BQ + BP + AP

= 9 cm + 6 cm + 6 cm + 5 cm + 5 cm + 7 cm + 7 cm + 9 cm

= 54 cm.