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Question
Prove that the line of centres of two intersecting circles subtends equal angles at the two points of intersection.
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Solution
Let two circles having their centres as O and O’ intersect each other at point A and B respectively. Let us join OO’.
In ΔAOO’ and BOO’,
OA = OB ...(Radius of circle 1)
O’A = O’B ...(Radius of circle 2)
OO’ = OO’ ...(Common)
ΔAOO’ ≅ ΔBOO’ ...(By SSS congruence rule)
∠OAO’ = ∠OBO’ ...(By CPCT)
Therefore, line of centres of two intersecting circles subtends equal angles at the two points of intersection.
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