Question

Prove that the line of centers of two intersceting circles subtends equal angles at the two points of intersceting.​

Answer 1

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Answer 2

Answer:

Step-by-step explanation:

Given : Two intersecting circles, in which OO′ is the line of centres and A and B are two points of intersection.

To prove : ∠OAO′ = ∠OBO′

Construction : Join AO, BO, AO′ and BO′.

Proof : In ∆AOO′ and ∆BOO′, we have

AO = BO [Radii of the same circle]

AO′ = BO′ [Radii of the same circle]

OO′ = OO′ [Common]

∴ ∆AOO′ ≅ ∆BOO′ [SSS axiom]

⇒ ∠OAO′ = ∠OBO′ [CPCT]

Hence, the line of centres of two intersecting circles subtends equal angles at the two points of intersection. Proved.