If a chord AB subtends an angle of 60° at the center of a circle, then angle between the tangents at A and B is also 60°.


False


Consider the problem in above diagram. In which we have a circle with center O and AB be any chord with AOB = 60°


Now,


OA AC and OB CB [ As tangent to at any point on the circle is perpendicular to the radius through point of contact]


OBC = OAC = 90° [1]


In Quadrilateral AOBC [ By angle sum property of quadrilateral]


OBC + OAC + AOB + ACB = 360°


90° + 90° + 60° + ACB = 360°


ACB = 120° [2]


So the angle between two tangents is 120°. So the above statement is false .


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