Question

Explain the proof:

Equal chords of a circle subtend equal angles at the centre.

Answer 1

Given => Let ' O ' Be The Centre Of The Circle . Line AB And Line CD Are Two Equal Chords And Angle AOB And Angle COD Are The Angles Subtended By The Chords At The Centre .

R.T.P => Angle AOB Is Congruent To Angle COD .

Construction => Join The Centre To The Points Of Each Chord And You Get Two Triangles ∆AOB And ∆COD .

Proof =>
In Triangles AOB And COD ..

AB = CD [ Given ]
OA = OC [ Radii Of Same Circle ]
OB = OD [ Radii Of Same Circle ]

Therefore ∆AOBIs Congruent To ∆COD [ SSS Congruency ]

Thus Angle AOB Is Congruent To Angle COD [ CPCT ] .

Hence Proved ...!

Answer 2

Hey Mate __!!

Given,

AB = CD (Equal chords)

To prove,

∠AOB = ∠COD

Proof,

In ΔAOB and ΔCOD,

OA = OC (Radii)
OB = OD (Radii)
AB = CD (Given)

∴ ΔAOB ≅ ΔCOD (SSS congruence condition)

Thus, ∠AOB = ∠COD by CPCT.

Equal chords of congruent circles subtend equal angles at their centres.

Thanks__!!