AB is a diameter of a circle with centre O, CB is a tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 6 cm and AG = 8 cm, then the length of BC is:

Solution (By Examveda Team)

$$\eqalign{ & \Delta AGB \sim \Delta BGC \cr & \frac{{AB}}{{BC}} = \frac{{BG}}{{GC}} = \frac{{AG}}{{BG}} \cr & \frac{{12}}{{BC}} = \frac{{4\sqrt 5 }}{{GC}} = \frac{8}{{4\sqrt 5 }} \cr & GC = 10 \cr & \frac{{12}}{{BC}} = \frac{{4\sqrt 5 }}{{10}} \cr & BC = 6\sqrt 5 \cr} $$