Multiple choice

Two chords AB and CD of a circle with centre O intersect at P. If (\angle APC = 40^{0}). Then the value of (\angle AOC + \angle BOD) is

  1. $50^{0}$
  2. $60^{0}$
  3. $80^{0}$
  4. $120^{0}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

When two chords intersect at point P inside a circle, the angle between them (∠APC = 40°) is half the sum of the measures of the arcs intercepted by the angle and its vertical angle. The central angles ∠AOC and ∠BOD subtend these arcs. The relationship is: ∠AOC + ∠BOD = 2 × ∠APC = 2 × 40° = 80°.

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