A tangent is drawn at a point P on a circle. A line through the centre O of a circle of radius 7 cm cuts the tangent at Q such that PQ = 24 cm. Find OQ.
25cm
Given OP = 7 cm (Radius), PQ = 24
Since tangent at a point on the circle is perpendicular to the radius to the point.
∴OP⊥OQ
In right angled triangle OPQ,
OQ2=OP2+PQ2 (By Pythagoras theorem)
OQ2=72+242
OQ2=49+576
OQ2=625
OQ=√625=25 cm