The length of the common chord of two intersecting circles is 24 cm. If the diameter of the circles is 30 cm and 26 cm, then the distance between the centers (in cm) is:
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Correct answer: B
Explanation
The correct answer is Option 2 i.e. 14 cm.
Radius = Diameter/2
Radius of first circle = 30/2 = 15 cm
Radius of second circle = 26/2 = 13 cm
Applying Pythagoras theorem
In triangle ACM
⇒ AM2 = AC2 - CM2
⇒ AM2 = 152 - 122
⇒ AM2 = 225 - 144
⇒ AM2 = 81
⇒ AM = 9
Now, in triangle CBM
⇒ MB2 = CB2 - CM2
⇒ MB2 = 132 - 122
⇒ MB2 = 169 - 144
⇒ MB2 = 25
⇒ MB = 5
⇒ AB = AM - MB = 9 + 5 = 14 cm