Question

Equal chords of a circle subtend equal angle on centre.

• A. True
• B. False

Answer 1

The correct option is A True

Let us consider two chords of a circle with centre O as shown the two chords be$AB$ and $CD$

As given in this question two chords are equal so

$AB=CD$

To prove:$\angle AOB=\angle DOC$

Now let us consider the$△AOB$ and $△DOC$

$AO=OD$ (radius of the circle )

$AB=CD$ ( given )

$ OB = OC (radius of circle )

$\therefore \Delta AOB\cong \Delta DOC$ (SSS congruency rule )

$\therefore \angle AOB=\angle DOC$

Hence, poved