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Question

In the above figure, O is the centre of the circle, FD is a tangent at C.Then, which of the following statements are true?


Correct Answer
A
ABC=90
Correct Answer
B
ACB=30
Correct Answer
C
ACD=90
Your Answer
D
ABC=110

Solution

The correct options are
A ABC=90
B ACB=30
C ACD=90

ACD=90      [Tangent at any point of a circle and the radius through this point are perpendicular to each other)
ACD=ABC=90           [Angles in alternate segments are equal]
The angle between a tangent and a chord through the point of contact is equal to an angle in the alternate segment.

Consider ΔABC,
BAC+ACB+ABC=180
60+ACB+90=180           [Given, BAC=60]             
ACB=180150ACB=30
  Options (a), (b), (c) are true.

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