two chords AB and CD of a circle that's centre is O . Make equal angles with the radius through A
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Step-by-step explanation:
Given, ∠AEQ=∠DEQ
OL⊥AB,OM⊥DC
In △OLE and △OME
∠OLE=∠OME (Both 90
o
)
∠OEL=∠OEM (given, ∠AEQ=∠DEQ)
OE=OE (common)
∴△OLE≅△OME (AAS congruence)
OL=OM (CPCT)
OL is the distance of chord AB from centre and OM is the
distance of chord CD from centre.
Since, OL=OM
chord AB and CD are equidistant from centre
Hence, AB=CD (chords at equal distance from centre)
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