MathematicsIf A and B are two points on a circle such that the measure of arc AB is 260 °  . What will be a possible value for the angle subtended by arc BA at a point on the circle?

If A and B are two points on a circle such that the measure of arc AB is 260 °  . What will be a possible value for the angle subtended by arc BA at a point on the circle?


  1. A
    100 °  
  2. B
    75 °  
  3. C
    50 °  
  4. D
    25 °   

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    Solution:

    It is given that A and B are two points on a circle such that AOB   = 260 °   .
    Suppose point C is on the circle as shown in the figure.
    It is known that m ( AOB= 260 ° )   then, AOB= 360 ° 260 ° = 100 °  .
    The angle subtended by chord AB at the center is twice that as subtended at the point C. So, ACB =  AOB 2 = 100 ° 2 = 50 °  .
    Therefore, the correct option is (3).
     
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