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Question

In the given figure, there are two circles that touch each other at A. P is a point which is at a distance of 25 cm from O as shown in the figure. The radius of the circle with centre O is 7 cm. The diameter of the circle with centre O’ is 10 cm. What is the length of the tangent PC?


A

25 cm

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B

24 cm

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C

26 cm

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D

27 cm

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Solution

The correct option is B

24 cm






In the given figure, PO=25 cm and OA=7 cm
We know that the tangent is perpendicular to the radius at the point of contact
So, POA=90.
Hence, applying pythagoras theorem, we have PO2=AO2+PA2
252=72+PA2
Hence, PA2=62549=576
PA=24 cm
Now, considering the circle with centre O' alone



We know that PA=24 cm. Now PA and PC are tangents from an external point P to the same circle. Hence, they are equal in length.
Thus, PC=PA=24 cm.


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