In given figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, $∠$ B = $90^{\circ}$ and DS = 5 cm, then the radius of the circle is ___ cm.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
11

Let radius of the circle = r

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

BP = BQ = r ...... (OQBPis a square)

AQ = 29 - r

DS = DR = 5 cm

$∴$ AR = AD – DR = 23 cm – 5 cm = 18 cm

But, AQ = AR

29 - r = 18

r = 11 cm

Suggest Corrections

Similar questions

In the given figure, a circle with centre O, is inscribed in a quadrilateral ABCD such that it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, $∠$ = $90^{o}$ and DS = 5 cm then find the radius of the circle.

Q. In the given figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90° and DS = 5 cm, then the radius of the circle (in cm) is

(a) 11 (b) 18 (c) 6 (d) 15 [CBSE 2013]

Q. In the given figure, a circle with centre O, is inscribed in a quadrilateral ABCD such that it touches the side BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90^∘ and DS = 5 cm then find the radius of the circle. [CBSE 2008, 13]

Q. In Fig 2, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB=29 cm, AD=23 cm,

∠ 90^{\circ}

and DS= 5 cm, then the radius of the circle (in cm.) is:

In Fig., a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P,Q,R and S respectively, If AB = 29 cm, AD = 23 cm, $D B = 90^{\circ}$ and DS = 5 cm, then the radius of the circle (in cm.) is :

Join BYJU'S Learning Program

In given figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, ∠B = 90∘ and DS = 5 cm, then the radius of the circle is ___ cm.

The correct option is A 11 Let radius of the circle = r We know that the lengths of the tangents drawn from an external point to a circle are equal. BP = BQ = r ...... (OQBPis a square) AQ = 29 - r DS = DR = 5 cm ∴ AR = AD – DR = 23 cm – 5 cm = 18 cm But, AQ = AR 29 - r = 18 r = 11 cm

In given figure, a circle with centre O is inscribed in a quadrilateral ABCD such that, it touches the sides BC, AB, AD and CD at points P, Q, R and S respectively. If AB = 29 cm, AD = 23 cm, $∠$ B = $90^{\circ}$ and DS = 5 cm, then the radius of the circle is ___ cm.