Answer :

Let PQ and RS be two equal chords of a given circle and they are intersecting each other at point T

To prove: PT = RT

QT = ST

Draw perpendiculars OV and OU on these chords.

In ΔOVT and ΔOUT,

OV = OU (Equal chords of a circle are equidistant from the centre)

∠OVT = ∠OUT (Each 90°)

OT = OT (Common)

ΔOVT ΔOUT (RHS congruence rule)

VT = UT (By CPCT) (i)

It is given that,

PQ = RS (ii)

PQ = RS

PV = RU (iii)

On adding (i) and (iii), we get

PV + VT = RU + UT

PT = RT

On subtracting equation (iv) from equation (ii), we obtain

PQ − PT = RS − RT

QT = ST

Therefore, PT = RTQT = ST

hence proved

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