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

i. What is d(O, P) = ? Why? 

ii. If d(O, Q) = 8 cm, where does the point Q lie? 

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

1 Answer

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Best answer

i. seg OP is the radius of the circle. 

∴ d(0, P) = 9 cm 

ii. Here, 8 cm < 9 cm 

∴ d(0, Q) < d(0, P) 

∴ d(0, Q) < radius Point Q lies in the interior of the circle. 

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

d(0, 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 [Taking square root of both sides] 

∴ PR = √144

∴ PR  = 12 cm

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