Question

Which of the following statements is not true?

विकल्प

• If a point P lies inside a circle, no tangent can be drawn to the circle, passing through P.

• If a point P lies on the circle, then one and only one tangent can be drawn to the circle at P.

• If a point P lies outside the circle, then only two tangents can be drawn to the circle from P.

• A circle can have more than two parallel tangents, parallel to a given line.

Answer 1

A circle can have more than two parallel tangents, parallel to a given line.

Explanation:

(a) True, a point inside a circle cannot lie on any tangent; every line through an interior point meets the circle in two points.

(b) True, at a point on the circle there is exactly one tangent; it is perpendicular to the radius at the point of contact.

(c) True, from a point outside the circle exactly two tangents can be drawn to the circle.

(d) False, for a given direction (a given line slope) a circle has at most two tangents parallel to that direction, so it cannot have more than two parallel tangents.

Hence the statement that is not true is a circle can have more than two parallel tangents, parallel to a given line.