In the given figure, two identical circles of radius 4 cm touch each other. A and B are the centres of the two circles. If RQ is a tangent to the circle, then what is the length (in cm) of RQ?

Solution (By Examveda Team)

n² = 8 × 16
n² = 128
n = 8$$\sqrt 2 $$

b = (8$$\sqrt 2 $$ + a)
a² + (16)² = b²
a² + (16)² = (8$$\sqrt 2 $$ + a)²
a² + 256 = 128 + a² + 16$$\sqrt 2 $$ a
128 = 16$$\sqrt 2 $$ a
a = $$\frac{8}{{\sqrt 2 }}$$
a = 4$$\sqrt 2 $$