Question : The length of the common chord of two intersecting circles is 24 cm. If the diameter of the circles are 30 cm and 26 cm, then the distance between the centres (in cm) is:
Option 1: 16 cm
Option 2: 14 cm
Option 3: 18 cm
Option 4: 12 cm
Correct Answer: 14 cm
Solution :
The length of the common chord = 24 cm
Diameter of the 1st circles = 30 cm
Radius of 1st circle = 15 cm
Diameter of 2nd circle = 26 cm
Radius of 2nd circle = 13 cm
The line joining the centres bisects the common chord. So, $AD = \frac{AB}{2}$
Length of $OD = \sqrt{AO^2-AD^2}$
= $\sqrt{15^2-12^2}$
= $\sqrt{225-144}$
= $\sqrt{81}$
= 9
Length of $PD = \sqrt{AP^2-AD^2}$
= $\sqrt{13^2-12^2}$
= $\sqrt{169-144}$
= $\sqrt{25}$
= 5
Thus, OP = OD + PD
= 9 + 5
= 14
Hence, the correct answer is 14 cm.
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