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Question

Determine the angle AOC, if CBA=25o and O is the centre of the circle.


A
30o
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B
40o
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C
50o
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D
60o
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Solution

The correct option is C 50o
The angle subtended by the diameter to any point on the circle is equal to 90o.

From the given figure,


ACB is the angle subtended by the diameter on the circle.
ACB=90o

CAB=180o(CBA+90o)
CAB=180o25o90o=65o

For ACO, the sides AO and CO are radii of the circle.
Hence, CAO=ACO
Also, CAO+ACO+AOC=180o
2CAO+AOC=180o
AOC=180o2CAO
AOC=180o2×65o=50o

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Angle Subtended by the Diameter to any Point on the Circle is equal to 90 degrees
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