prove: a circle with O had chord AB congruent to chord CD also CD is perpendicular to AB and On is perpendicular to chord CD
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Answer:
∠OMN=∠ONM (Hence Proved)
Step-by-step explanation:
Given: AB and CD are equal chords of a circle whose center is O. OM is perpendicular to AB and ON is perpendicular to CD.
To prove: ∠OMN=∠ONM
Figure: Please see the attachment
Theorem: If chords are equal of same circle then they are equidistance from center.
AB = CD
OM is distance of chord AB from center.
ON is distance of chord CD from center.
OM=ON (If chords are equal of same circle then they are equidistance from center)
In ΔMON, OM=ON
∠OMN=∠ONM , In a triangle if opposite sides are equal then their corresponding angles are equal.
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