A straight line is drawn cutting two equal circles and passing through the midpoints M of the line joining their centers O and O'. Prove that the chords AB and CD, which are intercepted by the two circle are equal.
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Hey Dear here is Your answer =)
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Draw OP⊥AB and O'Q⊥CD.Consider
ΔOPM and ΔO'QMOM = O'M [Given]
∠OMP = ∠O'QM [Vertically opposite angles]
∠OPM = ∠O'QM = 90° [Construction]
∠POM = ∠QO'M [Angle sum property of a triangle]
So, ΔOPM ≅ ΔO'QMOP = O'Q [CPCT]⇒ AB = CD [Equal chords of same circle or equal circles are equidistance from the centers of the respective circles.]
Hence proved.
_________________________________________________________
Hope it helps You Out =)
Thanks .... (^^)
___________________________________________________________
Draw OP⊥AB and O'Q⊥CD.Consider
ΔOPM and ΔO'QMOM = O'M [Given]
∠OMP = ∠O'QM [Vertically opposite angles]
∠OPM = ∠O'QM = 90° [Construction]
∠POM = ∠QO'M [Angle sum property of a triangle]
So, ΔOPM ≅ ΔO'QMOP = O'Q [CPCT]⇒ AB = CD [Equal chords of same circle or equal circles are equidistance from the centers of the respective circles.]
Hence proved.
_________________________________________________________
Hope it helps You Out =)
Thanks .... (^^)
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