Two circles of radii 15 cm and 12 cm interest each other, and the length of their common chord is 18 cm. What is the distance (in cm) between their centers?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 12 + 3√7.
Radius = 15 cm and 12 cm
Common chord PQ = 18 cm
PQ will be perpendicular to the line joining centers OO’.
Hence, PR = PQ/2 = 9 cm
We can apply Pythagoras's theorem in triangles POR and PO’R:
RO = √(152-92)
= √(225-81)
= √144 = 12 cm
RO’ = √(122-92)
= √(144-81)
= √63 = 3√7 cm
Hence,
OO’ = [12 + 3√7] cm