Question

Prove that if chords of congruent circles
subtend equal angles at their centres then the chords are equal​

Answer 1

${ \large{ \boxed{ \red{ \underline{ \bf \:Consider\: the\: following \:diagram }}}}}$

From above it is given that ∠AOB = ∠COD i.e. they are equal angles.

Here, we will have to prove that the line

segments AB and CD are equal i.e. AB = CD.

${ \large{ \sf{ \underbrace{\underline{\bigstar \:Proof:}}}}}$

In triangles AOB and COD,

∠AOB = ∠COD (as given in the question)

OA = OC and OB = OD (As these are the radii of the circle)

By SAS congruency, ΔAOB ≅ ΔCOD.

$\textbf{As a result by the rule of CPCT, AB = CD. (Hence proved)}$

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