AB and CD are equal chords …
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Gaurav Seth 3 years, 9 months ago
AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E. Prove that EB = ED and AE = CE.
<hr />Given: AB and CD are equal chords of a circle whose centre is O. When produced, these chords meet at E.
To Prove: EB = ED and AE = CE.
Construction: From O draw OP ⊥ AB and OQ ⊥ CD. Join OE.
PE - PB = QE - QD
EB = ED Proved.
BE + AB = ED + CD 
AE = CE
Proof: ∵ AB = CD | Given
∴ OP = OQ
| ∵ Equal chords of a circle are equidistant from the centre
Now in right ∆s OPE and OQE,
Hyp. OE = Hyp. OE | Common
Side OP = Side OQ | Proved above
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