Question

Fill in the blanks:

(i) The common point of a tangent and the circle is called ..........

(ii) A circle may have .............. parallel tangents.

(iii) A tangent to a circle intersects in it ............ point(s).

(iv) A line intersecting a circle in two points is called a ...........

(v) The angle between tangent at a point on a circle and the radius through the point is ........

Answer 1

(i) We know that the tangent to a circle is that line which touches the circle at exactly one point. This point at which the tangent touches the circle is known as the ‘point of contact’.

Therefore we have,

The common point of the tangent and the circle is called Point of contact.

(ii) We know that the tangent is perpendicular to the radius of the circle at the point of contact. This also means that the tangent is perpendicular to the diameter of the circle at the point of contact. The diameter of the circle can have at the most one more perpendicular line at the other end where it touches the circle. The perpendicular line at the other end of the diameter is the tangent.

Also we know that two lines which are perpendicular to a common line will be parallel to each other.

Therefore,

A circle may have two parallel tangents.

(iii) From the very basic definition of tangent we know that tangent is a line that intersects the circle at exactly one point. Therefore we have,

A tangent to a circle intersects it in one point.

(iv) From the definition of a secant we know that any line that intersects the circle at 2 points is a secant. Therefore, we have

A line intersecting a circle in two points is called a secant.

(v) One of the properties of the tangent is that it is perpendicular to the radius at the point of contact. Therefore,

The angle between the tangent at the point of contact on a circle and the radius through the point is 90°.