MathematicsIn the figure below, AOB is the diameter of the circle and C, D, E are any three points on the semi-circle. Then what is the value of ∠ACD + ∠BED?

In the figure below, AOB is the diameter of the circle and C, D, E are any three points on the semi-circle. Then what is the value of ∠ACD + ∠BED?


  1. A
    240 °  
  2. B
    270 °  
  3. C
    260 °  
  4. D
    280 °   

    Fill Out the Form for Expert Academic Guidance!l



    +91



    Live ClassesBooksTest SeriesSelf Learning



    Verify OTP Code (required)

    I agree to the terms and conditions and privacy policy.

    Solution:

    Given that, AOB is a diameter of the circle and C,D,E   are any three points on the semi-circle.
    Joining AE, then we will find out that ACDE   is a cyclic quadrilateral.
     The sum of the opposite angles will be 180 °  .
    Also, the angle in a semicircle is 90 °  .
    So, Adding equation 1 and equation 2.
    ∠ACD+∠AED+∠AEB= 180 ° + 90 °   ∠ACD+∠AED+∠AEB= 270 °   ∠ACD+∠BED= 270 °   So, the value is ∠ACD+∠BED= 270 °  .
    Hence, option 2 is correct.
     
    Chat on WhatsApp Call Infinity Learn