In fig, AB and CD are two equal chords of a circle with centre O. If M and N are the midpoints of AB and CD respectively, prove that (a) ∠ ONM = ∠ ONM (b) ∠ AMN = ∠ CNM. M and N are mid points of equal diords AB and CD respectively. ON ⊥ CD and OM ⊥ AB ∴ ∠ ONC = ∠ OMA (90° each) ...(1) ∴ AB = CD ON = OM (equal chords are equidistant from the centre) In Δ MON , MO = NO ∴ ∠ ONM = ∠ OMN ..(2) Subtracting (2) from ( 1) ∠ONC - ∠ ONM = ∠ OMA - ∠ OMN ∠ CNM =∠ AMN Concept: Properties of Congruent Chords - Theorem: Equal chords of a circle are equidistant from the centre. Is there an error in this question or solution?
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