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

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Solution

We know that tangent from an external point to the circle are equal
so
RC=CQ=3cm
PB=BQ=5cm
AP=AS=6cm
SD=DR=4cm

perimeter of quadratic ABCD
=AB+BC+CD+DA
=(AP+PB)+(BQ+CQ)+(CR+DR)+(AS+SD)
=(6+5)+(5+3)+(3+4)+(6+4)
=11+8+7+10
=36cm

correct option is (c) 36cm

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Similar questions

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

A B C D

is circumscribed. The circle touches the sides

A B, B C, C D, D A

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respectively. If

A P = 9 c m, B P = 7 c m, C Q = 5 c m, D R = 6 c m

, find the perimeter of quad.

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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

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

Q. In the given figure, quad. ABCD is circumscribed, touching the circle at P, Q, R and S such that ∠DAB = 90°, If CS = 27 cm and CB = 38 cm and radius of the circle is 10 cm, then AB = ?

(a) 28 cm
(b) 21 cm
(c) 19 cm
(d) 17 cm

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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

We know that tangent from an external point to the circle are equal so RC=CQ=3cm PB=BQ=5cm AP=AS=6cm SD=DR=4cm perimeter of quadratic ABCD =AB+BC+CD+DA =(AP+PB)+(BQ+CQ)+(CR+DR)+(AS+SD) =(6+5)+(5+3)+(3+4)+(6+4) =11+8+7+10 =36cm correct option is (c) 36cm

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

We know that tangent from an external point to the circle are equal
so
RC=CQ=3cm
PB=BQ=5cm
AP=AS=6cm
SD=DR=4cm

perimeter of quadratic ABCD
=AB+BC+CD+DA
=(AP+PB)+(BQ+CQ)+(CR+DR)+(AS+SD)
=(6+5)+(5+3)+(3+4)+(6+4)
=11+8+7+10
=36cm

correct option is (c) 36cm