Question

Find the radius of circle O

Answer 1

We know tangent is perpendicular to radius of circle at point of contact .

Using Pythagoras theorem in triangle OPQ

OP^2 +RQ^2 = OQ^2

r^2 + 225 =( 9+r)^2

r^2 + 225 =81+18r+r^2

r^2 + 225 -81-18r - r^2 = 0

144-18r = 0

144 = 18r

r = 144/18

r = 8