If two chords of a circle AB and CD meet at right angles, show that the length of the arc AC plus the arc BD is equal to half the circumference of the circle.

Here i tried to prove that angle AOC and angle BOD = 180, where O is centre and hence arc lengths would be half the circumference. However i cannot do that.

I am pretty sure the approach of this question is using arc lengths and angles at centre.

However if any other approach is found that would be brilliant.