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Given: 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 and ST = QTConstruction: Draw OV⊥ PQ and OU ⊥ SR. Join OT.
Proof: In ΔOVT and ΔOUT, OV = OU (Equal chords of a circle are equidistant from the centre)OT = OT (Common )∴ ΔOVT ≅ ΔOUT ( R.H.S.)⇒ VT= UT (By CPCT )⇒ PV + VT = RU + UT (∵ AV = RU = ( ½ )PQ = (½) RS⇒ PT = RT⇒ PQ – PT = SR – RT (Given PQ = RS )⇒ QT= ST.
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