Circles ncert solutions Chapter 10 Exercise 10.2 Question 10
10. 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 segment joining the points of contact at the center.
Solution:
Given: AB and AC are two tangents to a circle.
To Prove:
Proof:
{Tangent is perpendicular to the radius of circle} (1)
{Tangent is perpendicular to the radius of circle} (2)
Also,
{Sum of interior angles of quadrilateral is equal to
}
Putting (1) and (2) in the above equation, we get
Hence Proved
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