# Changes

,  06:38, 15 February 2014
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= Hints for difficult problems =

= Hints for difficult problems =
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== Ex 4.4.2==
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#Suppose two chords of a circle are equidistant from the centre of the circle, prove that the chords have equal length.
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'''DATA''' :-  Let AB & CD are the two chords which are equidistant from the centre 'O'  of the circle.  [ Here OP is the perpendicular distance from  the centre O to the chord AB and OQ is the perpendicular distance from  the centre O to the chord CD] OP = OQ.
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'''TO PROVE :-''' AB = CD,
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'''CONSTRUCTION :-''' Join OA & OD.
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'''PROOF :-'''
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{[Consider  In ∆AOP & ∆DOQ
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OA = OD
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OP = OQ
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Angle APO = Angle DQO
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∆AOP ≡ ∆DOQ
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AP = DQ
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Let  AB = AP + BP
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= AP + AP
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= 2AP
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AB = 2DQ ---------- 1.
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and  CD = CQ + DQ
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= DQ + DQ
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CD = 2DQ --------- 2.
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From equtn 1 & equtn 2
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AB = CD
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Equi distances from circle
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SAS Axiom
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Acording to properties of  SAS axiom.
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Perpendicular drawn from centre to chord which
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bisect the chord, i.e. AP = BP.
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Perpendicular drawn from centre to chord which
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bisect the chord, i.e. CQ = DQ
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Acording to AXIOM-1]}
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{|class="wikitable"
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|Steps
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|Explanation
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|Write the step
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|Explanation for thestep
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= Project Ideas =

= Project Ideas =
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