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Let AB and CD be the equal chords.
Let O be the centre of circle.
Let E and F be the mid-points of the chords.
Therefore,
EB=AE
CF=DF
Equal chords are equidistant from the centre.
∴OE=OF
Now in △OAB and △OCD
OA=OD(Radius of circle)
AB=CD(Given)
OB=OC(Radius of circle)
By SAS congruency,
△OAB≅△OCD
Now by C.P.C.T.,
∠AOB=∠COD
Hence proved that the line joining the mid-point of two equal chords of a circle subtends equal angles with the chord.
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Step-by-step explanation:
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