If two equal chords of a …
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Gaurav Seth 5 years, 1 month ago
Given: A circle with centre O. Its two equal chords AB and CD intersect at E.
To prove: AE = DE and CE = BE.
Construction: Draw OM ⊥ AB and ON ⊥ CD. Join OE.
Proof: In ∆OME and ∆ONE,
OM = ON
| ∵ Equal chords of a circle are equidistant from the centre
OE = OE | Common
AM + ME = DN + NE
AE = DE
AB - AE = CD - DE
BE = CE | Given
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