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