A common internal tangent connecting two circles is 9 cm long. The distance between the circles' centers is 15 cm. If the larger circles has a radius of 8 cm, what is the radius of the smaller circle?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 4 cm.
Radius of larger circle (R) = 8 cm
Distance between centres (d) = 15 cm
Length of internal tangent = 9 cm
Length of internal tangent = √[d2 – (R + r)2]
⇒ 9 = √[152 – (8 + r)2]
⇒ 81 = 225 – (8 + r)2
⇒ (8 + r)2 = 144
⇒ 8 + r = 12
⇒ r = 12 - 8 = 4 cm