Question 2

Let's fill in the blanks based on our knowledge of circles and tangents.

Step 1 — Tangent intersection

Tangent: A line that touches a circle at exactly one point — it does not cross through the circle.

A tangent line touches a circle at only one point.

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

Step 2 — Line intersecting in two points

Secant: A line that cuts through a circle and intersects it at two distinct points, entering at one side and exiting at the other.

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

Step 3 — Parallel tangents

A circle can have tangents drawn at every point on it. However, for two tangents to be parallel, they must be drawn at the two opposite ends of a diameter. Since a circle has only one pair of "top and bottom" positions at any given orientation, a circle can have at most two parallel tangents.

(iii) A circle can have two parallel tangents at the most.

Step 4 — Common point name

Point of contact (or point of tangency): The single point where a tangent line meets the circle. It is the only point shared by both the tangent and the circle.

(iv) The common point of a tangent to a circle and the circle is called the point of contact.

Answer

(i) one (ii) secant (iii) two (iv) point of contact