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O is the center of a circle with a diameter 30 cm. P is a point outside the circle and PA is tangent of the circle, then find: (i) The length of tangent PA; if OP = 39 cm, (ii) The distance between O and P, if the length of the tangent PA is 20 cm.

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39 cm

36 cm

27 cm

25 cm

answer is B.

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Detailed Solution

Given that diameter = 30cm
As we know radius =

d i a m e t e r 2 = 15 cm

Let's denote the radius of the circle by r i.e. r = 15 cm
Since OP = 39 cm
In ∆OPA as we know

.
Now we have a right triangle with sides
OA (radius) = 15 cm, OP = 39 cm and PA
As we know, Pythagorean theorem can be used in right triangle
It follows,

O A 2 + P A 2 = O P 2

Substituting the given values we get

(15) 2 + P A 2 = (39) 2 P A 2 = 1521 − 225 P A 2 = 1296 P A = 1296 P A = 36 c m

AP = 36cm
So, the correct answer is Option 2.

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