In Fig. 10.72, PA and PB are tangents to the circle drawn from an external point P. CD are a third tangent touching the circle at Q. If PB = 10 cm and CQ = 2 cm, what is the length PC?

Given:


PB = 10 cm


CQ = 2 cm


Property: If two tangents are drawn to a circle from one external point, then their tangent segments (lines joining the external point and the points of tangency on circle) are equal.


Using the above property,


PA = PB = 10 cm (tangent from P)


And,


CA = CQ= 10 cm (tangent from C)


Now,


PC = PA – CA


= 10 cm – 2 cm


= 8 cm


Hence, PC = 8 cm


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