Circle geo helpp (1 Viewer)

[supR]

Thanks in advance

Question 13 from yr 12 3u, 9C

13.a - Prove that if two chords of a circle bisect each other, then they are both diameters.


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[pikachu975]

Thanks in advance

Question 13 from yr 12 3u, 9C

13.a - Prove that if two chords of a circle bisect each other, then they are both diameters.


Sent from my iPhone using Tapatalk

Let one chord be AB, and one be CD with the midpoints of both as M

AM x BM = CM x DM (product of intercepts of chords)
and AM = BM and CM = DM as they are both bisected
AM^2 = CM^2
AM = CM
So AM = BM = CM = DM

Hence these are all radii with M as the centre of the circle, hence both chords are diameters