Question

In the figure, AC is the diameter of circle, centre O. Chord BD is perpendicular to AC. Write down the angles p, q, r in term of x.

Answer 1

∠ ADB = `1/2 "∠ AOB" = x/2`
∠ ADB = 90° - r
∠ ADB = ∠ ACB = q

Combining these, we get
`x/2 = 90° - r = q`

⇒ 2r = 180° - x
and  x = 2q

∠ DAC = ∠ CAB
∠ DAC = ∠ BDC

⇒ p = r = `1/2` (180° - x)