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
Solution:
Let us consider the figure in which a circle with centre O and AB a chord with ∠AOB = 60°
As tangent to any point on the circle is perpendicular to the radius through the point of contact,
OA ⏊ AC and OB ⏊ CB
∠OBC = ∠OAC = 90° …(1)
Using angle sum property of quadrilateral in Quadrilateral AOBC,
∠OBC + ∠OAC + ∠AOB + ∠ACB = 360°
Substituting the values
90° + 90° + 60° + ∠ACB = 360°
So we get
∠ACB = 120°
Angle between two tangents is 120°.
Therefore, the statement is false.
✦ Try This: 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°.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.2 Problem 1
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
Summary:
The statement “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°” is false
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