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

Posted by Palak Rathore 3 years, 8 months ago

CBSE > Class 09 > Mathematics

2 answers

Palak Gupta 3 years, 8 months ago

Given: Two circles with centers A and B, which intersect each other at C and D. To prove : ∠ACB=∠ADB Construction : Join AC,AD,BD and BC. Proof : In triangles ACB and ADB, we have AC=AD ...Radii of the same circle BC=BD ...Radii of the same circle AB=AB ...Common Therefore, by SSS criterion of congruence, △ACB≅△ADB ⇒∠ACB=∠ADB ...CPCT

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Khushi Kaur 3 years, 8 months ago

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.Read more on Sarthaks.com - https://www.sarthaks.com/12080/prove-that-line-centres-intersecting-circles-subtends-equal-angles-points-intersection

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