# Question Video: Relating Points- Lines- and Circles in Space Mathematics

Consider a circle of center π with a radius π and a point π΄ on a line πΏ, where the line πΏ does not intersect the circle and line segment ππ΄ β₯ πΏ. Which of the following is true? [A] ππ΄ = π [B] ππ΄ < π [C] ππ΄ > π

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### Video Transcript

Consider a circle of center π with a radius π and a point π΄ on a line πΏ, where the line πΏ does not intersect the circle and line segment ππ΄ is perpendicular to πΏ. Which of the following is true? Is it (A) ππ΄ equals π, (B) ππ΄ is less than π, or (C) ππ΄ is greater than π?

To answer this question, letβs begin by drawing a sketch of the scenario. Hereβs our circle center π. Weβre given that it has a radius π units. In other words, consider a point π that lies anywhere on the circumference of the circle. The line segment joining the center of the circle to this point is π units. Then, we have this line πΏ that doesnβt intersect the circle. Point π΄ lies on the line, and weβre told that the line segment ππ΄ is perpendicular to πΏ. And so now we should be able to answer the question quite quickly.

We said that the length of line segment ππ is π units. Letβs define the length of the line segment between π and π΄ to be π₯ units. And we can quite quickly see just from the diagram alone that π₯ must be greater than π. Since π₯ is the length of line segment ππ΄, then weβre able to say that ππ΄ is greater than π. And so the answer is (C): ππ΄ is greater than π.

Now, in fact, this will be true for any point π΄ that lies outside of the circle. Since the radius is the length of the line segment that joins the center to a point on its circumference, if π΄ lies outside of the circle in any position, then it makes sense that the line segment between the center and π΄ is greater than the radius.