In the given figure, a circle with centre O, is inscribed in a quadril

1.	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.
Answer» In the given figure, O be the centre of circle which is inscribed in a quadrilateral ABCD. And OP = OQ = r = radius of circle The circle touches the sides of quadrilateral at P, Q, R and S respectively. AB = 29 cm, AD = 23 cm, ∠B = 90° DS = 5 cm Join OP and OQ. Now, OP = OQ = r and ∠B = 90° So, PBQO is a square. DR and DS are the tangents to the circle. DR = DS = 5 cm AQ and AR are tangents to the circle. AR = AD – DR = 23 – 5 = 18 cm AQ = AR = 18 cm And BQ = AB – AQ = 29 – 18 = 11 cm Since PBQO is a square. OP = OQ = BQ = 11 cm Hence, radius of the circle is 11 cm

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.

Answer»

In the given figure,

O be the centre of circle which is inscribed in a quadrilateral ABCD.

And OP = OQ = r = radius of circle

The circle touches the sides of quadrilateral at P, Q, R and S respectively.

AB = 29 cm, AD = 23 cm, ∠B = 90°

DS = 5 cm

Join OP and OQ.

Now,

OP = OQ = r and ∠B = 90°

So, PBQO is a square.

DR and DS are the tangents to the circle.

DR = DS = 5 cm

AQ and AR are tangents to the circle.

AR = AD – DR = 23 – 5 = 18 cm

AQ = AR = 18 cm

And BQ = AB – AQ = 29 – 18 = 11 cm

Since PBQO is a square.

OP = OQ = BQ = 11 cm

Hence, radius of the circle is 11 cm

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