Prove that the diameter of a circle perpendicular to one of the two parallel chords of a circle is perpendicular to the other and bisects it

Asked by pereiracalida | 14th Jan, 2018, 06:43: PM

Expert Answer:

 
begin mathsize 16px style Chord space AB parallel to Chord space CD
Diameter space PQ perpendicular AB
Now comma space diameter space of space straight a space circle space always space passes space through space the space centre space of space the space circle.
rightwards double arrow Diameter space PQ space is space perpendicular space bisector space of space AB comma
But space PQ perpendicular AB space and space AB parallel to CD
rightwards double arrow PQ perpendicular CD
Thus comma space PQ 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 PQ space is space perpendicular space bisector space of space CD. end style

Answered by Rashmi Khot | 15th Jan, 2018, 10:35: AM