AB and CD are two parallel chords of a circle and line l is the perpendicular bisector of AB. Show that l is the perpendicular bisector of CD also.

Asked by pereiracalida | 14th Jan, 2018, 06:41: PM

Expert Answer:

 
begin mathsize 16px style The space Perpendicular space bisector space of space any space chord space of space straight a space circle space always space passes
through space the space centre space of space the space circle.
Since space straight l space is space perpendicular space bisector space of space AB comma
rightwards double arrow straight l space passes space through space the space centre space of space the space circle.
But space straight l perpendicular AB space and space AB parallel to CD
rightwards double arrow straight l perpendicular CD
Thus comma space straight l space is space perpendicular space to space CD space and space passes space through space the space centre space of space the space circle.
rightwards double arrow straight l space is space perpendicular space bisector space of space CD. end style

Answered by Rashmi Khot | 15th Jan, 2018, 10:23: AM