Question

prove that the chords of a circle equidistant from the centre are congruent
pls prove with steps​

Answer 1

Step-by-step explanation:

IMAGINE A CIRCLE WITH GIVEN SPEC

 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)

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Answer 2

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