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deProve that AB CD2A straight line is drawn cutting two equalcircles and passing through the mid-point Mof the line joining their centres O and O'.o'Prove that the chords AB and CD, which anted hy the two circles, are equal.

Answer»

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'QM

OP = O'Q [CPCT]⇒ AB = CD [Equal chords of same circle or equal circles are equidistance from the centers of the respective circles.]Hence proved.



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