Question

prove that if chords of congruent circles spend equal angles at the centre then the chords are equal

Answer 1

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Let us consider two congruent circles (circles of same radius) with centres as O and O'.

In ΔAOB and ΔCO'D,

∠AOB = ∠COD (Given)

OA = OC (Radii of congruent circles)

OB = OD (Radii of congruent circles)

∴ ΔAOB ≅ ΔCOD (SAS congruence rule)

⇒ AB = CD (By CPCT)

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

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Answer 2

Answer:

Consider two congruent circles with centres as O and O

In AOB andCOD,

L AOB = L COD(given )

OA= OC(radius)

OB=OD(radius)

By SAS congruent rule

AOB=~ COD

Therefore, AB=CD(CPCT)

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

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