In figure, $O$ is the center of the circle. P Q is a tangent to the circle and secant PAB passes through the center O. If PQ=5cm and $PA = 1 cm,$ then find the radius of the circle.

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12 cm

10 cm

8 cm

14 cm

answer is C.

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Detailed Solution

Given that

O

is the center of the circle. P Q is a tangent to the circle and secant PAB passes through the center O.
We have to find the radius of the circle.
If a tangent segment and a secant segment are drawn to a circle from outside the circle, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its outside secant segment.
The required figure geometry is shown below,
Question Image

Since AOB is the diameter of the circle. So, AOB=PB-PA Here, PA is the segment of the secant POB outside the circle. Then, by using the tangent secant rule, A tangent segment and a secant segment are drawn to a circle from outside the circle, and then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its outside secant segment. Thus,