Enter the center of the circle, the point from which the tangent line is drawn, the radius of the circle, and the distance between the center of the circle and the point from which the tangent line is drawn into the calculator to determine the point of tangency.
Point Of Tangency Formula
The following formula is used to calculate the point of tangency on a circle.
(x, y) = (x1 + r * (y2 – y1) / d, y1 + r * (x1 – x2) / d)
Variables:
- (x, y) is the point of tangency
- (x1, y1) is the center of the circle
- (x2, y2) is the point from which the tangent line is drawn
- r is the radius of the circle
- d is the distance between the center of the circle and the point from which the tangent line is drawn
What is a Point Of Tangency?
A point of tangency is the exact spot where a line or curve (the tangent) touches another curve or surface without crossing it. In other words, it is the point where the tangent intersects the curve or surface. This point is significant in various fields such as mathematics, physics, and engineering, as it is often used in calculations and analyses related to curves and surfaces.
How to Calculate Point Of Tangency?
The following steps outline how to calculate the Point of Tangency using the given formula:
- First, identify the values of the variables in the formula:
- (x1, y1): the center of the circle
- (x2, y2): the point from which the tangent line is drawn
- r: the radius of the circle
- d: the distance between the center of the circle and the point from which the tangent line is drawn
- Next, substitute the values of the variables into the formula: (x, y) = (x1 + r * (y2 – y1) / d, y1 + r * (x1 – x2) / d)
- Then, perform the calculations to find the values of x and y.
- Finally, the calculated values of x and y represent the coordinates of the Point of Tangency.
Example Problem:
Use the following values as an example problem to test your knowledge:
(x1, y1) = (3, 5)
(x2, y2) = (7, 2)
r = 4
d = 6
