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In the adjoining figure, BC is a diamete...

In the adjoining figure, BC is a diameter of a circle with centre O. If AB and CD are two chords such that AB `||` CD, prove that AB=CD

Text Solution

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Draw `OL _|_ AB` and `OM _|_ CD`
`:. Delta OLB ~= Delta OMC [:' /_ OBL = /_ OCL , OB = OC =r ` and `/_ OLB = /_ OMC = 90^(@)` ]
`:. OL = OM`.
But, the chords equidistant from the centre are equal.
Hence, AB `=` CD.
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