Given:
A circle with center O is given. OA is the segment joining the center O to a point A on the circle. BC is the line touching the circle.
We need to determine the line that is tangent to the circle.
Option a: Line FG
The chord of the circle is a line that touches any two points on the circle.
From the figure, it is obvious that the line FG touches the points F and G on the circle.
Hence, the line FG is a chord of the circle.
Hence, Option a is not the correct answer.
Option b: Line DE
The secant of the circle is a line that intersects the circle at two points.
Hence, the line DE intersects the circle at two points.
Hence, the line DE is a secant.
Thus, Option b is not the correct answer.
Option c: Line OA
The radius of the circle is a line from the center of the circle to any point on the circle.
Thus, the line OA is drawn from the center of the circle to the point A on the circle.
Hence, the line OA is a radius of the circle.
Thus, Option c is not the correct answer.
Option d: Line BC
The tangent of the circle is the line that touches the circle at only one point.
Hence, the line BC touches the circle at only one point.
Hence, the line BC is a tangent to the circle.
Thus, Option d is the correct answer.