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.

# 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.

1. A
39 cm
2. B
36 cm
3. C
27 cm
4. D
25 cm

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### Solution:

Given that diameter = 30cm
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,

Substituting the given values we get

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

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