Question

Fill in the blanks:
(i). A tangent to a circle intersects it in ___________ point (s).
(ii). A line intersecting a circle in two points is called a ____________.
(iii). A circle can have _________ parallel tangents at the most.
(iv). A common point of a tangent to a circle and the circle is called ___________.

Answer 1

Hint: Here we have to fill the blanks which are related to circles.. We are going to use some relations of circles with lines to fill the above blanks.

Complete step-by-step answer:
               

We have to find the information to fill the given blanks.
By the definition of tangent, we get, a tangent to a circle is a straight line that touches the circle at one point.
By the definition of the circle we get, a circle is a locus of a point from a given point which is known as the centre of the circle.
From the diagram circle there is a tangent line $XY$ intersect a circle at only one point.
So, by the definitions we get, a tangent intersects a circle at only one point.
$\therefore $ The answer for the first blank is one.
By the definition of secant, we get, Secant is a line that intersects the circle in two points.
So, by the definition we get, a line intersecting a circle in two points is called a secant.
From the diagram circle there is a secant line is $AB$ that intersects the circle in two points.
$\therefore $ The answer for the second blank is secant.
Circle can have at most two parallel tangents, one at a point on it and the other at a point diametrically opposite to it.
Tangent at any point of a circle is perpendicular to the radius through the point of contact. Extended radius is a diameter which has two end points and hence two tangents which are parallel to themselves and perpendicular to the diameter.
From the diagram circle,
Center $O$, Diameter $AB$, Tangents $XY\& PQ$, and \[XY\parallel PQ\]
$A$ and $B$ are called as points of contact.
$\therefore $ The answer for the third blank is two numbers.
The point of the circle where the tangent is drawn is known as the point of tangent.
A common point of a tangent to a circle and the circle is called the point of contact.
$\therefore $ The answer for fourth blank is the point of tangent.
Hence,
A tangent to a circle intersects it in only one point.
A line intersecting a circle in two points is called a secant.
A circle can have two parallel tangents at the most.
A common point of a tangent to a circle and the circle is called the point of contact.

Note: Like this geometrical question, we must concentrate on what we have to find. Because some relations are the same. For example, a line intersecting a circle in two points is called a secant. We may go wrong, the sense of that is to be chord. So we have to be careful by the relations of geometrical relations.