In the given figure AB and DC are two chords of a circle with centre O, which when produced meet at P. If PB = 7 cm, BA = 10 cm and PO =12cm, find the radius of the circle.

12 cm

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10 cm

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6 cm

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5 cm

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Solution

The correct option is D
5 cm

Let the radius of the circle = r cm

$∴ O C = O D = r$

$P C = P O - O C = 12 - r$

$P D = P O + O D = 12 + r$

Chords AB and DC intersect at P (given)

$P A \times P B = P C \times P D$

$17 (7) = (12 - r) (12 + r)$

$119 = 144 - r^{2}$

$r^{2} = 25$

$r = 5 c m$

Hence (D)

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In the given figure AB and DC are two chords of a circle with centre O, which when produced meet at P. If PB = 7 cm, BA = 10 cm and PO =12cm, find the radius of the circle.

The correct option is D 5 cm Let the radius of the circle = r cm ∴OC=OD=r PC=PO–OC=12–r PD=PO+OD=12+r Chords AB and DC intersect at P (given) PA×PB=PC×PD 17(7)=(12–r)(12+r) 119=144–r2 r2=25 r=5 cm Hence (D)