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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.
Solution
∠ 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)
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