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In the given figure, O is the center of the circle and chord AB : chord CD = 5 : 3. If angle DOC = 60°; then ∠AOB is :

In the given figure, O is the center of the circle and chord AB : chord CD = 5 : 3. If angle DOC = 60°; then ∠AOB is : Circle, Concise Mathematics Solutions ICSE Class 9.
  1. 120°

  2. 75°

  3. 100°

  4. 80°

Circles

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Answer

Ratio of the angles subtended by the chords on the center is equal to the ratio of the chords.

AOBCOD=ABCDAOB60°=53AOB=53×60°=300°3=100°.\Rightarrow \dfrac{∠AOB}{∠COD} = \dfrac{AB}{CD} \\[1em] \Rightarrow \dfrac{∠AOB}{60°} = \dfrac{5}{3} \\[1em] \Rightarrow ∠AOB = \dfrac{5}{3} \times 60° = \dfrac{300°}{3} = 100°.

Hence, Option 3 is the correct option.

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