Question

prove that equal chords of congruent circles subtend equal angles at their centres.​

Answer 1

Answer:

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Let us consider two congruent circles (circles of same radius) with centers as O and O

In ΔAOB and ΔCO'D,

AOB = CO'D (Given)

OA = O'C (Radii of congruent circles)

OB = O'D (Radii of congruent circles)

ΔAOB ΔCO'D (SAS congruence rule)

AB = CD (By CPCT)

Hence, if chords of congruent circles subtend equal angles at their centers, then the chords are equal

Hope it helps u ✌

Answer 2

QUESTION -

Consider two congruent circles having centre O and O' and two chords AB and CD of equal lengths.

ANSWER -

Consider two congruent circles having

centre O and O' and two chords AB and CD of equal lengths.

(as shown in attachment)

In ΔAOB and ΔCO'D,

AB = CD (Chords of same length)

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.