Thread: [SOLVED] Finding the Radius of Circle Given the Tangent Line and a Center Point

Problem:
(h , k) = 4,11
Tangent Line:

What I Want To Know:
How do you determine the radius?

Description:
I couldn't find what I was looking for in the book, so the past 20 minutes I've been trying to solve it with what I understand. The distance from the center point and the tangent line will be the shortest possible distance between the center point and any point on the line. The line segment I believe will be perpendicular so the slope of the line segment should be the negative reciprocal. Knowing this I would need to find out when the perpendicular line meets the center point and at what point the line touches the tangent line.

Pretty much I think I solved it while typing the description

At least if my logic is straight.

What is best way to determine this?

Originally Posted by Altermeris

Pretty much I think I solved it while typing the description

At least if my logic is straight.

What is best way to determine this?

Your reasoning is good. You know the slope of the normal line (this is the line perpendicular to the tangent line), and you know a point that belongs to it, so you can use the point-slope equation.

Afterwards, find the point of tangency (which will be the intersection of the tangent and normal) and then use Pythagorean theorem to calculate distance from center to point of tangency.