Question : Two circles of radius 13 cm and 15 cm intersect each other at points A and B. If the length of the common chord is 24 cm, then what is the distance between their centres?
Option 1: 12 cm
Option 2: 16 cm
Option 3: 14 cm
Option 4: 18 cm
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Correct Answer: 14 cm
Solution :
Given: Two circles of radius 13 cm and 15 cm with centres O and P intersect at A and B.
OP is the distance between the centres of circles.
AB intersects OP at Q.
AB = 24 cm
AQ = BQ= $\frac{24}{2}$
= 12 cm
$OQ= \sqrt{(OA^2-AQ^2)}$
$=\sqrt{(13^2-12^2)}= 5$
$PQ= \sqrt{(AP^2-AQ^2)}$
$=\sqrt{(15^2-12^2)}= 9$
$OP= OQ+PQ= 5+9= 14$
Hence, the correct answer is 14 cm.
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