In the given figure, PA and PB are tangents to the circle drawn from an external point P.


In the given figure, PA and PB are tangents to the circle drawn from an external point P. CD is a third tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length PC?


Given data is as follows:

PB = 10 cm

CQ = 2 cm

We have to find the length of PC

We know that the length of two tangents drawn from the same external point will equal. Therefore,


It is given that PB = 10 cm

Therefore, PA = 10 cm

Also, from the same principle we have,


It is given that CQ = 2 cm

Therefore, CA = 2cm

From the given figure we can say that,

PC = PA − CA

Now that we know the values of PA and CA, let us substitute the values in the above equation.

PC = 10 − 2

PC = 8 cm

Therefore, length of PC is 8 cm.


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