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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?
Solution
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]
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