Question

Line ℓ touches a circle with centre O at point P. If radius of the circle is 9 cm, answer the following.

If d(O, R) = 15 cm, how many locations of point R are line on line l? At what distance will each of them be from point P?

Answer 1

There can be two locations of point R on line l.

d(O, R) = 15 cm

Now, in ∆OPR, ∠OPR = 90°    ......[Tangent theorem]

∴ OR² = OP² + PR²    ......[Pythagoras theorem]

∴ 15² = 9² + PR²

∴ 225 = 81 + PR²

∴ PR² = 225 – 81 = 144

∴ PR = `sqrt(144)`

= 12 cm

∴ Each location of point R will be at a distance of 12 cm from point P.    ......[Taking square root of both sides]