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unile theproperty which you have observed.Tous write the proof of this propertyTheorem: perpendicular drawn from the centre of a circle on its chord bisects the chordTo prove i seg APE seg BPseg AB is a chord of a circle with centre oseg Op 1 chord ABGivenPB: Draw seg OA and seg ORIn A OPA and AOPBLOPA ZOPBseg Op I chord ABsog OP = seg OPcommon sidehypotenuse OA hypotenuse OBradii of the same circle... A OPA = A OPB hypotenuse side theoremseg PA seg PB0.3.0.1.Fig. 6.4 |
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Answer» Answer: To PROVE that the perpendicular from the centre to a chord BISECT the chord. Consider a CIRCLE with centre at O and AB is a chord such that OX perpendicular to AB To prove that AX=BX In ΔOAX and ΔOBX ∠OXA=∠OXB [both are 90 ] OA=OB (Both are radius of circle ) OX=OX (common side ) ΔOAX≅ΔOBX AX=BX (by property of congruent triangles ) hence proved. |
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