The length of the common chord of two intersecting circles is 30 cm. If the radii of the two circles are 25 cm and 17 cm,find the distance between their centres.

30 cm

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25 cm

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35 cm

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28 cm

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Solution

The correct option is D
28 cm

Given AB = 30 cm

OA =25 cm

AP = 17 cm

From figure we can see that OP is perpendicular to AB

⇒ AC = CB
∴ AC = CB = 15 cm

In ΔACP, $A P^{2} = P C^{2} + A C^{2}$ [Using Pythagoras theorem]
⇒ $17^{2} = P C^{2} + 15^{2}$
⇒ $P C^{2} = 289 - 225 = 64$
⇒ PC = 8 cm

Similarly in ΔACO, by Pythagoras theorem OC = 20 cm

OP = OC + OC

= 20 + 8

= 28 cm

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