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From Karnataka Open Educational Resources
→Hints for difficult problems
= 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]}
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= Project Ideas =
= Project Ideas =
