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.
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 = √ (by pythagoras theorem)
OR = 6cm
similarly, we can show pythagoras theorem in triangle PBR.