Prove that the equal chords of …
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Posted by Ñoßi Ţä 5 years, 2 months ago
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Rohit Kumar 5 years, 2 months ago
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Gaurav Seth 5 years, 2 months ago
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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