Two circles with centers P and Q of radii 6 cm and 4 cm, respectively, touch each other internally. If the perpendicular bisector of PQ meets the bigger circle in A and B, then the value of AB is:
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 2 cm.
Given that
Two circles with centres P and Q of radii 6 cm and 4 cm, respectively, touch each other internally.
PQ = 6 - 4 = 2 cm
PS = PQ/2 = 2/2 = 1 cm
In triangle APS,
⇒ AS2 = AP2 - PS2
⇒ AS2 = 62 - 12 = 36 - 1 = 35
⇒ AS = √35 cm
Hence, AB = 2AS = 2 √35 cm