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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^{\circ} at the centre of a circle, then angle between the tangents at A and B is also 60^{\circ}.

Answers (1)

Answer False

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 angle between the tangents at A and B is 120^{\circ}.

Therefore the given statement is False.


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