Question 1157991

*[illustration CENTRAL1.png]
Perpendicular to chord from centre bisects chord
AD=BD=8

Triangle AOD right triangle

By Pythagoras theorem

12^2= 8^2+OD^2

OD = 4sqrt(5)

tan B = 4sqrt(5)/8 = 1.12

Angle B = 48.2 ~48 deg

In triangle AOD 

angle A +angle AOD +angle ODA =180 deg
48+90+AOD =180
Angle AOD =42 deg
Angle AOC = 2* 42 =84

84 is central angle
Measure of arc AC =84 degrees