In circle geometry, to prove three points are collinear, say A,B,C, do you have to prove that AB and BC are part of a cyclic quad? Then you prove AB and BC are supplementary.
Or can you just prove directly that AB and BC are supplementary
Two chords AB and CD bisect each other at X. Show that this is not possible unless X is the center.
NO idea how to approach this one as well.
Show that in a circle, a shorter chord is always further from the centre than a longer chord.
AB, CD and XY are chords in a circle with centre O. XY cuts AB and CD in L and M, which are the midpoints of AB and CD. Prove that XY is greater than either AB or CD.
I hav no idea how to approach this problem