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.

Answer 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

Answer 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