The length of the common chord of two intersecting circles

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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 centre (in cm) is

1. 13
2. 14
3. 15
4. 16

Correct Option: B

On the basis of question we draw a figure of two circles with centres O and O' ,

Here , d₁ = 30 cm and d₁ = 30 cm
From ∆AOD and ∆AO'D ,
OD = √15² - 12²
OD = √225 - 144
OD = √81 = 9 cm
O'D = √13² + 12²
O'D = √169 - 144
O'D = √25
O'D = 5 cm
∴ OƠ = OD + O'D = 9 + 5 = 14 cm