A circle is inscribed in a quadrilateral ABCD where ∠B = 90. If AD = 24 cm,

AB = 30 cm and DS = 8 cm, find the radius ‘r ‘ of the circle.

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A circle is inscribed in a quadrilateral ABCD where ∠B = 90. If AD = 24 cm,

AB = 30 cm and DS = 8 cm, find the radius ‘r ‘ of the circle.

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solve it similarly

Solution. Since tangents to a circle is perpendicular to the radius through the point.

OPB = Ð OQB = 90°

It is given that Ð B = 90°. Also, OP = OQ. Therefore, OPBQ is a square.

Since tangents drawn from an external point to a circle are equal in length.

DR = DS [Tangents from D]

AR = AQ [Tangents from A]

And BP = BQ [Tangents from B]

Now, DR = DS

DR = 5 [Q DS = 5 cm (given)]

AD – AR = 5

23 – AR = 5

AR = 23 – 5 = 18

AQ = 18 [AR = AQ]

AB – BQ = 18

29 – BQ =18 [Q AB = 29 cm (given)]

BQ = 29 -18 = 11