Let PQ and RS be two equal chords of a given circle and they are intersecting each other at point T.
draw perpendiculars OV and OU on these chords.
in triangle OVT and in triangle OUT,
OV=OU (equal chords of a circle are equidistant from the centre)
angle OVT=angle OUT ( each 90')
therefore: triangle OVT is congruent to triangle OUT (RHS congruence rule)
therefore: VT=UT (by CPCT)....(1)
it is given that,
=> 1/2 PQ=1/2 RS
on adding equations (1) and (3), we obtain
on subtracting equation (4) from equation (2), we obtain
=> QT = ST.....(5)
equations (4) and (5) indicate that the corresponding segments of chords PQ and RS are congruent to each other.