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Question -

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



Answer -

Consider the followingdiagram

In ╬ФPOOтАЩ and ╬ФQOOтАЩ

OP = OQ┬а┬а┬а┬а┬а┬а┬а┬а┬а(Radius of circle 1)

OтАЩP = OтАЩQ┬а┬а┬а┬а┬а┬а┬а(Radius of circle 2)

OOтАЩ = OOтАЩ┬а┬а┬а┬а┬а┬а┬а(Common arm)

So, by SSS congruency,╬ФPOOтАЩ тЙЕ ╬ФQOOтАЩ

Thus, тИаOPOтАЩ = тИаOQOтАЩ (proved).

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