Two circles of the same radius 6 cm, intersect each other at P and Q. If PQ = 10cm, then what is the distance between the centers of the two circles?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 2√11cm.
Given that
Two circles of the same radius 6 cm, intersect each other at P and Q.
If PQ = 10 cm
The radius OP = PK = 6 cm
PS = PQ/2 = 10/2 = 5 cm
In triangle PSO,
⇒ OS2 = OP2 - PS2
⇒ OS2 = 36 - 25
⇒ OS2 = 11
⇒ OS = √11 cm
Similarly, In triangle PSK,
SK = OS = √11 cm
Hence, the distance between centers of circles OK = OS + SK = √11 + √11 = 2√11 cm