Question

Recall that two circle are congruent if they have that same radii. Prove that equal chords of congruent circles substend equal at their center.​

Answer 1

Answer:

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. Hence, equal chords of congruent circles subtend equal angles at their centres.

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Answer 2

Answer:-

★ Given:-

▪︎Two congruent circle with center O and P.

▪︎Two equal chords AB and CD.

★ To Prove:-

• ∠ AOB = ∠ CPD

★ Construction:-

• Join OA

• Join OB

• Join PC

• Join PD

★ Theorem Used:-

▪︎Two circle are congruent if they have the same length of radii.

★ Proof:-

In ∆ AOB and ∆ CPD

• OA = PC [ Same radii of congruent ∆ ]

• OB = PD [ Same radii of congruent ∆ ]

• AB = CD [ Given ]

∆ AOB ≅ ∆ CPD ( By S.S.S. Congruence Rule )

∴ ∠ AOB = ∠ CPD [ C.P.C.T. ]

Hence, Proved.