AQ and BQ are tangents to a circle which meets at point Q externally outside the circle. If length of tangent AQ = 8 cm and shortest distance from the point on circle to point Q is 4 cm. then find radius of the circle?

The shortest distance from an external point Q to the circle is along the line through the center, which equals radius + shortest distance. Tangent length AQ = 8, shortest distance from circle to Q = 4, so the distance from Q to center = r + 4. By Pythagorean theorem: (r+4)^2 = r^2 + 8^2, giving r^2 + 8r + 16 = r^2 + 64, so 8r = 48 and r = 6.