Theorem of Equal Chords Subtending Equal Angles at the Center
Question 1Pro...
Question
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 ΔAOO′andBOO′, OA = OB (Radius of circle with centre O) O'A = O'B (Radius of circle with centre O') OO' = OO'(Common) ΔAOO′≅ΔBOO′ (By SSS congruence rule) ∠OAO′=∠OBO′(ByCPCT) Therefore, line of centres of two intersecting circles subtends equal angles at the two points of intersection.