Equal chords of a circle are equidistant from centre

Asked by admin @ 23/08/2021 in Math viewed by 292 People

Proof that equal chords are equidistant from the centre

Answered by admin @ 23/08/2021

In the figure,

Given:- A circle with centre O and chords AB = CD

Construction:- Draw OP⊥ AB and OQ ⊥ CD

Hence, AP = BP = (1/2)AB and CQ = QD = (1/2)CD

Also ∠OPA = 90° and ∠OQC = 90°

Since AB = CD,

⇒ (1/2) AB = (1/2) CD

⇒ AP = CQ

In ΔOPA and ΔOQC,

∠OPA = ∠OQC = 90°

AP = CQ (proved)

OA = OC (Radii)

Therefore, ΔOPA ≅ ΔOQC (By RHS congruence criterion)

Hence OP = OQ (CPCT)

So, equal chords are equidistant from the centre
is proved.

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