Multiple choice

In a circle, chords AD and BC meet at a point E outside the circle. If ∠BAE = 70° and ∠ADC = 110°, then ∠AEB is equal to?

  1. 70O

  2. 60O

  3. 30O

  4. 40O
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Using cyclic quadrilateral theorem, opposite angles sum to 180 degrees. From ∠BAE = 70°, chord AB subtends 70° at E, so arc ACB = 2×70° = 140°. Thus ∠ADC (opposite angle on circle) subtends arc ABC = 360° - 140° = 220°, giving ∠ADC = 110°. For exterior point E: ∠AEB = 180° - (∠BAE + ∠ABE). Since ∠ABE = 180° - ∠ADC = 70°, we get ∠AEB = 180° - (70° + 70°) = 40°.

Keep practicing — related questions