SSC CGL 2014 Tier 1 26 Oct shift 4

Question 137

AC is a chord of circle whose centre is at 0. If B is any point on the arc AC and ∠OCA = 20°, then the magnitude of ∠ABC is

Solution

OC=OA=radius .Hence , the angles opposite to these sides must also be equal.
So, ∠OCA=20 = ∠OAC. Hence , ∠AOC = 180 - 20 -20 = 140.
Now consider a point D on the major at of AC and join D to A & C. This gives △ADC.
So . ∠AOC= 2*∠ADC So, ∠ADC= 140/2 = 70
Now , ADCB is a cyclic quadrilateral sum of whose all opposite is 180.
So, ∠D + ∠B = 180 .
∠B = 180 - 70 = 110.




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