# If two equal chords of a circle intersect within the circle , prove that the segments of one chord are equal to the corresponding segments of the other chord.

1
by Ayon

2015-03-14T20:00:56+05:30
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')
OT=OT(common)
therefore: triangle OVT is congruent to triangle OUT (RHS congruence rule)
therefore: VT=UT (by CPCT)....(1)
it is given that,
PQ=RS....(2)
=> 1/2 PQ=1/2 RS
=> OV=RU....(3)
on adding equations (1) and (3), we obtain
PV+VT=RU+UT
=> PT=RT....(4)
on subtracting equation (4) from equation (2), we obtain
PQ-PT=RS-RT
=> QT = ST.....(5)
equations (4) and (5) indicate that the corresponding segments of chords PQ and RS are congruent to each other.
Thank you so much
ur welcome :)
hey ayon in equation (3) it is not OV=RU it is PV=RU sorry for the mistake :)