The angle between two tangents to a circle may be 0°. Write ‘True’ or ‘False’ and justify your answer
Solution:
It might be possible if both tangent lines coincide or parallel to each other.
Therefore, the statement is true.
✦ Try This: Prove that the angle between the two tangents drawn from an external point to a circle is supplementary to the angle subtended by the line segments joining the points of contact at the centre.
From the figure, PA and PB are the tangents which are drawn from P to a circle with centre O
OA and OB are the line segments drawn
The tangent to a circle is perpendicular to the radius through the point of contact
PA ⊥ OA
∠OAP = 90°
PB ⊥ OB
∠OBP = 90°
So we get
∠OAP + ∠OBP = (90° + 90°) = 180° .......(1)
The sum of all the angles of a quadrilateral is 360°.
∠OAP + ∠OBP + ∠APB + ∠AOB = 360° .....(2)
From equations (1) and (2),
∠APB + ∠AOB = 180°
Therefore, it is proved.
☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 10
NCERT Exemplar Class 10 Maths Exercise 9.2 Problem 4
The angle between two tangents to a circle may be 0°. Write ‘True’ or ‘False’ and justify your answer
Summary:
A circle is a two-dimensional figure formed by a set of points that are at a constant or at a fixed distance (radius) from a fixed point (center) in the plane. The statement “The angle between two tangents to a circle may be 0°” is true
☛ Related Questions:
- If angle between two tangents drawn from a point P to a circle of radius a and centre O is 90°, then . . . .
- If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60°, then . . . .
- The tangent to the circumcircle of an isosceles triangle ABC at A, in which AB = AC, is parallel to . . . .