Question

Prove equal chord of a circle subtends equal angle at centre​

Answer 1

The Proof for "Equal chord of a circle subtends equal angle at the Center".

Explanation:

Consider a Circle with center as C,

Radius AC ,BC ,DC and EC

Chord AB = Chord CD

To Prove:

"Equal chord of a circle subtends equal angle at center".

i.e ∠ACB = ∠ECD

Proof:

In Δ ABC and Δ DEC

Chord AB ≅ Chord DE .….{Given}

AC ≅ DC …..{Radius of Same Circle}

BC ≅ EC ….{Radius of Same Circle}

Δ ABC ≅ Δ DEC ….{By Side-Side-Side Congruence Postulate}

∴∠ACB ≅ ∠ECD ...{Corresponding Parts of Congruent Triangles are Congruent or CPCTC} ....Proved

i.e Equal chord of a circle subtends equal angle at the Center.