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Question

In Fig. 8.63, AB is a chord of length 16cm of a circle of radius 10cm. The tangents at A and B intersect at a point P. Find the length of PA.


Solution

OB=10cm
AB=16cm
OP is perpendicular to AB
so, AB is bisected into 2 equal parts.
PA = PB [lengths of tangents to a circle from external point are equal.]

Let, PA = PB = x
also R is point of intersection from perpendicular P to AB.

In triangle ORB

OR = 10064 (by pythagoras theorem)

OR = 6cm


similarly, we can show pythagoras theorem in triangle PBR.

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