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If a diameter AB of a circle with centre O bisects each of the two chords CD and EF as shownin the figure, Prove that the two chords are parallel |
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Answer» Given Diameter AB bisect chords CD and EF , So;CM = MDAndEN = NF And we know if a line from center to chord is bisecting that chord ,then that line is also perpendicular to that chord . So;OM⊥CD and ON⊥EFSo,∠OMC =∠OMD =∠ONE =∠ONF = 90°And∠OMC +∠ ONE = 180° ------ ( 1 ) These are consecutive interior angles .And finally, equation (1) is satisfied only if; CD | | EF , Where MN is transversal line .So,CD | | EF ( Hence proved ) |
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