Question 4

Tangent: A line that touches a circle at exactly one point (point of tangency) without crossing through it. It is always perpendicular to the radius at the point of contact.

Secant: A line that intersects a circle at two distinct points, passing through the interior of the circle.

Key construction idea: Any line parallel to AB will be perpendicular to the line drawn through O perpendicular to AB. So we draw that perpendicular from O, then: a line through the point where it meets the circle gives a tangent (touches at one point), and a line through a point inside the circle on that same perpendicular gives a secant (cuts at two points).

We need to draw a circle, a tangent, and a secant, all parallel to a given line.

Step 1 — Set up the drawing

Let's draw a circle. Let its center be O. Now, draw a straight line. Let's call this line AB.

Step 2 — Draw the perpendicular line

We will draw a line through O. This line must be perpendicular to AB. Let this perpendicular line intersect AB at point P. This line OP is important.

Step 3 — Find points for the lines

Now, let's extend the line OP. We need a point on the circle. This point must also be on the line OP. Let's call this point X. X is the point of tangency. Now, we need a point inside the circle. This point must also be on the line OP. Let's call this point Y. Y will help us draw the secant.

Step 4 — Draw the parallel lines

We will draw a line through X. This line must be parallel to AB. Let's call this line CD. CD is our tangent line. Now, we will draw another line through Y. This line must also be parallel to AB. Let's call this line EF. EF is our secant line.

Answer

(i) CD is the tangent line parallel to AB. (ii) EF is the secant line parallel to AB.