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Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.

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Data: Two circles having centres A and B, intersect at C and D. 

To Prove: ∠ACB = ∠ADB. 

Construction: Join A and B. 

Proof: 

In ∆ABC and ∆ABD, 

AC = AD (∵ radii of same circle are equal) 

BC = DD 

AB is common. 

∴ ∆ABC ≅ ∆ABD (SSS Postulate.) 

∴ ∠ACB = ∠ADB.

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