If a diameter AB of a circle with centre O bisects each of the two cho

1.	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.
Answer» Given Diameter AB bisect chords CD and EF , So CM = MDAndEN = NF And we know a line from center to chord is bisect that chord than that line also perpendicular on that chord . So OM⊥CD and ON⊥EFSo,∠OMC =∠OMD =∠ONE =∠ONF = 90° And∠OMC +∠ ONE = 180° ------ ( 1 ) These are consecutive interior angles , Only satisfied equation 1 true if CD \| \| EF , Where MN is transversal line .So,CD \| \| EF ( Hence proved )

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.

Answer»

Given Diameter AB bisect chords CD and EF , So

CM = MDAndEN = NF

And we know a line from center to chord is bisect that chord than that line also perpendicular on that chord . So

OM⊥CD and ON⊥EFSo,∠OMC =∠OMD =∠ONE =∠ONF = 90°

And∠OMC +∠ ONE = 180° ------ ( 1 )

These are consecutive interior angles , Only satisfied equation 1 true if

CD | | EF , Where MN is transversal line .So,CD | | EF ( Hence proved )