If a diameter of  a circle bisects each of the two chords of a circle, then prove that the chords are equal.

Asked by pereiracalida | 10th Jan, 2018, 06:51: PM

Expert Answer:

 
Your question is incorrect. It should be as follows:
If a diameter of  a circle bisects each of the two chords of a circle, then prove that the chords are equal.
 
begin mathsize 16px style AB space and space CD space are space two space equal space chords space of space straight a space circle space with space centre space straight O.
PQ space is space straight a space diameter space bisecting space chords space AB space and space CD space at space straight M space and space straight N space respectively.
Now comma space the space line space joining space the space centre space of space straight a space circle space to space the space mid minus point space of space straight a space chord space
is space perpendicular space to space the space chord.
rightwards double arrow OM perpendicular AB space and space ON perpendicular CD
rightwards double arrow angle AMO equals 90 degree space and space angle DNO equals 90 degree
rightwards double arrow angle AMO equals angle DNO
But space these space are space alternate space angles.
rightwards double arrow Chords space AB space and space CD space are space parallel space to space each space other. end style
 

Answered by Rashmi Khot | 11th Jan, 2018, 09:19: AM