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ABCD is a quadrilateral such that angle D = 90°. A circle touches the sides AB, BC, CD and DA at P, Q, R and S respectively If BC = 24 cm, CD = 25 cm and BP = 6 cm. Find the radius of circle.

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ABCD is a quadrilateral such that angle D = 90°. A circle touches the sides AB, BC, CD and DA at P, Q, R and S respectively If BC = 24 cm, CD = 25 cm and BP = 6 cm. Find the radius of circle.
1). 7 cm
2). 13 cm
3). 17 cm
4). 6 cm


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We use the property that the lengths of pair of tangents from an external point are equal.

Then BP = BQ = 6 cm

QC = BC - BQ = 24 - 6 = 18 cm

CR = QC = 18 cm (tangents from an external point are equal)

RD = CD - CR = 7 cm = SD (tangents from an external point are equal)

Now, angle D = 90°

Let the centre of circle be O.

Then, angle R and angle S in the quadrilateral ORDS is also 90°.

∴, ORDS is a square.

⇒ OR = DS = 7 cm = Radius

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