Question

THEOREM : Equal chords of a circle are equidisiant from the centre........................... PROVE IT..........................

Answer 1

Answer:

Given a circle with centre O and chords AB = CD

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 Δ’s OPA and OQC,

∠OPA = ∠OQC = 90°

AP = CQ (proved)

OA = OC (Radii)

∴ ΔOPA ≅ ΔOQC (By RHS congruence criterion)

Hence OP = OQ (CPCT)