Question

theorem 10.6 : if equal chords of a circle are congruent circles are equidistant from the centre or Centre then prove two congruent circles with this theorem

Answer 1

Answer:

Step-by-step explanation:

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)