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In the given figure, O is the centre of ...

In the given figure, O is the centre of a circle in which chords AB and CD intersect at P such that PO bisects `/_BPD`. Prove that `AB `=` CD .

Text Solution

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Draw `OE_|_AB` and `OF _|_ CD`.
Then, `/_ OEP = /_ = 90^(@) , OP = OP , /_ OPE = /_ OPF`.
`:. Delta OEP = ~= DeltaOFP`, and hence `OE = OE`. And , chords which are equidistant from the centre are equal.
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