Question

Question 2
Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

Answer 1

Let us consider two congruent circles (circles of the same radius) with centres as O and O'.

In $\Delta AOB$ and $\Delta C{O}^{\prime }D$,
$\angle AOB=\angle C{O}^{\prime }D$ (Given)
OA = O'C(Radii of congruent circles)
OB = O'D (Radii of congruent circles)
$\therefore \Delta AOB\cong \Delta C{O}^{\prime }D$ (SAS congruence rule)
$\Rightarrow AB=CD\left(ByCPCT\right)$
Hence, if chords of congruent circles subtend equal angles at their centres, then the chords are equal.