In the given figure, the circle touches the sides AB, BC, CD and DA of a quadrilateral ABCD at the points P, Q, R, S respectively. If AB = 11 cm, BC =x cm, CR = 4 cm and AS = 6 cm, the value of x is

___ cm.

Open in App

Solution

AP = AS = 6 cm

BP = BA – AP = 11 – 6 = 5

BQ = BP = 5

CQ = CR = 4

x = CQ + BQ

x = 4 + 5 = 9 cm

Suggest Corrections

Similar questions

In the given figure, the circle touches the sides AB, BC, CD and DA of a quadrilateral ABCD at the points P, Q, R, S respectively. If AB = 11 cm, BC =x cm, CR = 4 cm and AS = 6 cm, the value of x is

___ cm.

Q. In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its side AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm , find x

Q. In the given figure, a circle touches all the four sides of a quadrilateral

A B C D

whose sides

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

and

C D = 4 c m

, find

A D

Q. In the given figure, a quadrilateral ABCD is drawn to circumscribe a circle such that its sides AB, BC, CD and AD touch the circle at P, Q, R and S respectively. If AB = x cm, BC = 7 cm, CR = 3 cm and AS = 5 cm, then x =

(a) 10 (b) 9 (c) 8 (d) 7 [CBSE 2014]

Q. In the given figure ABCD is a quadrilateral in which

D = 90^{\circ}

. A circle C(O,r) touches the sides AB , BC , CD and DA at P , Q , R and S, respectively. If BC = 38cm , CD = 25 cm and BP =27cm then find the value of r.

Join BYJU'S Learning Program

In the given figure, the circle touches the sides AB, BC, CD and DA of a quadrilateral ABCD at the points P, Q, R, S respectively. If AB = 11 cm, BC =x cm, CR = 4 cm and AS = 6 cm, the value of x is ___ cm.

AP = AS = 6 cm BP = BA – AP = 11 – 6 = 5 BQ = BP = 5 CQ = CR = 4 x = CQ + BQ x = 4 + 5 = 9 cm

In the given figure, the circle touches the sides AB, BC, CD and DA of a quadrilateral ABCD at the points P, Q, R, S respectively. If AB = 11 cm, BC =x cm, CR = 4 cm and AS = 6 cm, the value of x is

___ cm.

AP = AS = 6 cm

BP = BA – AP = 11 – 6 = 5

BQ = BP = 5

CQ = CR = 4

x = CQ + BQ

x = 4 + 5 = 9 cm