Question

Which of the following is correct ?

• A. Chords making equal angles at the center of the circle are equal to each other.
• B. Equal chords of same circle can make unequal angles at the center of the circle.

Answer 1

The correct option is A Chords making equal angles at the center of the circle are equal to each other.

When the end ponts of equal chords joined by the radii to the center of circle they always make equal angles at the center of the circle.

Here, angles made at the center are equal,
$\angle AOC=\angle BOC$ and chords associated to these angles are $AC$ and $BC$. Here, $AC=BC$
Hence, equal chords of same circle cannot make unequal angles at the center of the circle.

So, option $\left(a\right)$ correct.