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  • Write ‘True’ or ‘False’ and justify your answer in each of the following : If a chord AB subtends an angle of 60° at the centre of a circle, then angle between the tangents at A and B is also 60°.

Write ‘True’ or ‘False’ and justify your answer in each of the following :
If a chord AB subtends an angle  60^{\circ} at the center of a circle, then the angle between the tangents at A and B is also 60^{\circ}.

Answers (1)

Answer False
Solution
              
Here CA and CB are the two tangents which is drawn on chord AB and also we know that tangent and radius are perpendicular to each other.
i.e., \angle CBO=\angle CAO= 90^{\circ}
In quadrilateral, ABCD
\angle A+\angle B+\angle C+\angle O= 360^{\circ}
[\mathbb{Q}  Sum of interior angles of a quadrilateral is 360^{\circ}]
90^{\circ}+90^{\circ}+\angle C+60^{\circ}= 360^{\circ}
\angle C= 360^{\circ}-60^{\circ}-90^{\circ}-90^{\circ}
\angle C= 120^{\circ}
Here we conclude that the angle between the tangents at A and B is 120^{\circ}.

Therefore the given statement is False.


       

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infoexpert27

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