❥ Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
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Answer:
Therefore, two circles are congruent if they have equal radius. Consider two congruent circles having centre O and O' and two chords AB and CD of equal lengths. Hence, equal chords of congruent circles subtend equal angles at their centres.
Explanation:
chords of a circle AB and CD. We need to prove that AOB = COD In AOB and COD , we have AO = CO (Radius of the circle) BO = DO (Radius of the circle) AB = CD (Equal chords)By SAS criterion of congruence, we have AOB COD AOB = COD
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Brainly.in
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"Question 1 Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres. Class 9 - Math - Circles Page 173"
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Two circles are said to be congruent if and only if their radii are equal.=========================================================Let AB & CD are two equal chords of two congruent circles with Centre O and O’. i.e AB= CD. To Prove: ∠AOB = ∠CO'D Proof: In ΔAOB and ΔCO'D, AB = CD ( given) OA = O'C (Radii of congruent circles) OB = O'D (Radii of congruent circles) ΔAOB ≅ ΔCO'D (SSS congruence rule) ∠AOB = ∠CO'D (By CPCT) Hence, equal chords of congruent circles subtend equal angles at their centres.==========================================================Hope this will help you....
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Careers360
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Q: 1 Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
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Doubtnut
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Recall that two circles are congruent if they have the same radii. Prove that equalchords of congruent circles subtend equal angles at their centres.
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Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.
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Sarthaks eConnect
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Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
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Given : Two congruent circles with centres O and O′. AB and CD are equal chords of the circles with centres O and O′ respectively. To Prove : ∠AOB = ∠COD Proof : In triangles AOB and COD, AB = CD [Given] AO = CO ' BO = DO ' [Radii of congruent circle] ⇒ ∆AOB ≅ ∆CO′D [SSS axiom] ⇒ ∠AOB ≅ ∠CO′D Proved. [CPCT]
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Meritnation
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Recall that two circles are congruent if they have same radii Prove that equal chords of congruent circles subtend equal angles at their centres
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Dear Students Two circles are said to be congruent if and only if their radii are equal Let AB & CD are two equal chords of two congruent circles with Centre O and O’ i e AB= CD To Prove: ∠AOB = ∠CO'D Proof: In ΔAOB and ΔCO'D, AB = CD (given) OA = O'C (Radii of congruent circles) OB = O'D (Radii of congruent circles) ΔAOB ≅ ΔCO'D (SSS congruence rule) ∠AOB = ∠CO'D (By CPCT) Hence, equal chords of congruent circles subtend equal angles at their centres Regards
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Sarthaks eConnect
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Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
Answer · 1 vote
Data : Two circles having centres O and O’ and having equal radius. Chord AB = CD. To Prove: Equal chords of congruent circles subtend equal angles at their centres. Or ∠AOB = ∠CO’D Proof: In ∆AOB and ∆CO’D, OA = O’C (Data) OB = O’D (Data) AB = CD (Data) ∴ ∆AOB ≅ ∆CO’D ∴ ∠AOB = ∠CO’D.
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Vedantu
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Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
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Hint: To prove that they subtend equal angles it is enough to show that the triangles are congruent to each other by any of the rule examples SAS, AAA, SSS. After proving that congruent then by corresponding parts of congruent triangle theorem the subtend angles are equal. Complete step-by-step answer:The following are the schematic diagram of the two circles having the same radii. Since, two circles are congruent $ {C_1} $ and $ {C_2} $ .We know that $ AB $ is the chord of $ {C_1} $ and $ PQ $ is the chord of $ {C_2} $ .Since, it is given that two chords are equal so $ AB = PQ $ .The main aim is to prove that angles subtended by chords are equal, that is $ \angle AOB = \angle PXQ $ .To show that first let us prove that $ \Delta AOB \cong \Delta PO'Q $ .In the $ \Delta AOB $ and $ \Delta PO'Q $ ,Since the radius of congruent circles are equal,So, $ AO = PO' $ ….(1)Since the radius of congruent circles are equal, $ BO = QO' $ ……..(2)It is given that two chords are equal so, $ AB = PQ $ …
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OneClass
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Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
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Recall that two circles are congruent if they have the same radii. Prove that equal chords of congruent circles subtend equal angles at their centres.
✒ Let us consider a circle with center O and two equal chords of a circle AB and CD.
We need to prove that ∠AOB=∠COD
In △ AOB and COD, we have
AO=CO (Radius of the circle)
BO=DO (Radius of the circle)
AB=CD (Equal chords)
By SAS criterion of congruence, we have
△AOB≅△COD