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Iftne cequal chords of a circle intersect within the circle, prove that the segments ofhord are equal to corresponding segments of the other chord. |
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Answer» 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 = QT Construction:Draw OV⊥PQand 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.Hence proved Because it is given that = 2 equal chords of a circleIf think about diameter is equal in circle so, when they intersect the corresponding segment are equal |
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