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टु)- बिद०७०- Fot सील्ख . 92७, मौन S pidbe पेले=q oall o जहर e (‘d’\/\ S Q,\'\O’{c;\ q-

Answer»

Given that : AB and CD are two equal chords. And, M, N are mid point of chord AB and CD respectively.

To prove : ∠AMN=∠CNM and ∠BMN=∠DNM

Construction : Join OM and ON

Proof :Since the line segment joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.

Since AB and CD are equal chords, they are equidistant from the other. i.e., OM =ON

In ΔOMN,OM=ON (Proved)∠OMN=∠ONM (Angles opposite to equal sides) .....1∠OMA=∠ONC (each 90°) .....2 ∠OMB=∠OND (each 90°) .....3Subtracting 2 from 1, we have,∠OMA-∠OMN=∠ONC-∠ONM⇒∠AMN=∠CNMAdding 1 and 3, we have,∠OMB+∠OMN=∠OND+∠ONM⇒∠BMN=∠DNMHence Proved.



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