MathematicsIn given figure O is the center of the circle, BD = OD, and CD ⊥ AB. Find ∠BDC  .

In given figure O is the center of the circle, BD = OD, and CD ⊥ AB. Find ∠BDC  .


Diagram Description automatically generated

  1. A
    50 °  
  2. B
    30 °  
  3. C
    60 °  
  4. D
    40 °   

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    Solution:

    Given that, BD is the chord of the circle with center O. The radius is OD and AOB ⊥  AB.
    Diagram Description automatically generatedThe radius is, OD=OB=BD.
    We know when all three sides of the triangle are equal then the equilateral triangle. And also, all angles in equilateral triangle are equal to 60 °  .
    So, ∠OBD= 60 °  .
    Using the sum of angles in a triangle is 180 °   .
    ∠ABD+∠BDC+ 90 ° = 180 °   From the give figure,
    ∠ABD+∠BDC+ 90 ° = 180 °   60 ° +∠BDC+ 90 ° = 180 °   ∠BDC= 180 ° − 150 °   ∠BDC= 30 °  
    Hence, option 2 is correct.
     
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