circle

7. AB = 16, AN = 8, so NB = 16 - 8 = 8, that is AN = NB. CD is perpendicular to AB. By property of chord, center of circle must be on CD, that means CD is diameter of circle, since CD = 20, so radius = 20/2 = 10.
8.Let OC intersects AB at N. By property of chord, AN = NB = 24/2 = 12. OB = radius of circle = 13.
By Pythagoras thm., distance between center and chord AB = ON = sqrt (13^2 - 12^2) = sqrt (169 - 144) = sqrt 25 = 5.
9.
Since CN = CD/2, N is the mid-point of CD, by property of chord, ON is perpendicular to CD.
Since AB = CD, by property of chord, OM = ON, so triangle OMN is an isos. triangle, therefore, angle OMN = (180 - 45)/2 = 67.5