Question

O is the centre of the circle. ? ∠OCA = x°. 

a. Find ∠OAC 

b. Prove that ∠OCA + ∠ABC = 90° 

c. Prove that ∠ADC – ∠OCA = 90°

Answer 1

1. ∠OAC = x

2. ∠AOC = 180 - 2x

\(\angle B=\frac{180-2x}{2}=90-x\)

∠OCA + ∠ABC = x + 90 - x = 90°

3. ∠ADC = 180 - (90 - x) = 90 + x

∠ADC - ∠OCA = 90 + x - x = 90°