Question

From a point inside the circle how many secants can be drawn to the circle?
(a) 0
(b) 1
(c) 2
(d) Infinite

Answer 1

Hint: We will use the definition of secant to solve this question. A secant is a line that cuts through a circle such that it touches at two points of the circumference.

Complete step-by-step answer:
Before proceeding with the question we should understand the concept of secants in a circle.
A straight line that intersects a circle at two points is called a secant line. A chord is the line segment that joins two distinct points of the circle. A chord is a unique secant line and every secant line defines a unique chord. Secant means ‘to cut’ extracted from a Latin word ‘secare’. While in a circle, a secant will touch the circle in exactly two points and a chord is the line segment defined by these two points, that is the interval on a secant whose endpoints are these two points.
So from the above definition, there can be infinite secants which can be drawn to the circle.

Hence the correct answer is option (d).

Note: Remembering the definition of the secant is the key here. We in a hurry can make a mistake and may think that for a point outside the circle the number of secants that can be drawn is infinite so for the point inside the circle it should be 0 and hence we need to be clear with the definition.