Question

Two equal chords of the circle maketriangles when their end points are joined to the center of circle with radii.

Answer 1

In the above figure the two equal chords $AB$ and $CD$ are given which are joined to the center with the radii.
Now, the triangles so formed are $△AOB$ and $△COD$.

In $△AOB$ and $△COD$
$AO=CO$ (radius of same circle)
$BO=DO$ (radius of same circle)
$AB=CD$ (chords are equal)

So, $△AOB\cong △COD$ (SSS)

Hence, the triangles so formed are always congruent.