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Question
In the given figure, O is the center of the circle and AB is a tangent at B. If AB = 15 cm and AC = 7.5 cm, calculate the radius of the circle.
Solution 1
AB = 15 cm, AC = 7.5 cm
Let 'r' be the radius of the circle.
∴ OC = OB = r
AO = AC + OC = 7.5 + r
In ΔAOB,
AO2 = AB2 = OB2
(7.5 + r)2 = 152 + r2
`=> ((15 + 2r)/2)^2 = 225 + r^2`
`=>` 225 + 4r2 + 60r = 900 + 4r2
`=>` 60r = 675
`=>` r = 11.25 cm
Therefore, r = 11.25 cm
Solution 2
AB2 = AC × AD ...(PT2 = PA × PB)
`=>` 152 = 7.5 × AD
`=>` AD = `225/7.5` = 30
`=>` CD = AD – AC
= 30 – 7.5
= 22.5
∴ Radius = `1/2` × CD
Radius = `1/2` × 22.5
Radius = 11.25 cm
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