Question:
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?
Solution:
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,
PB = PA
It is given that PB = 10 cm
Therefore, PA = 10 cm
Also, from the same principle we have,
CQ = CA
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.