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Question 1
Prove that 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 ΔAOOandBOO,
OA = OB (Radius of circle with centre O)
O'A = O'B (Radius of circle with centre O')
OO' = OO'(Common)
ΔAOOΔBOO (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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