In the given figure, two identical circles of radius 4 cm touch each other. A and B are the centres of two circles. If RQ is a tangent to the circle, then what is the length (in cm) of RQ?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e 4√2
In the figure,
AP = AO + OP = 4 + 8 = 12 cm and AS = 4 cm
∴ PS2 = 122 – 42
⇒ PS = 8√2 cm
Now triangles ASP and RQP are similar;
∴ AS/RQ = SP/QP
⇒ 4/RQ = 8√2/16
⇒ RQ = 64/8√2
⇒ RQ = 4√2 cm