Point of Tangency Calculator

Calculate Point of Tangency









Formula

To calculate the point of tangency on a circle:

\[ (x, y) = \left( x1 + \frac{r \times (y2 - y1)}{d}, y1 + \frac{r \times (x1 - x2)}{d} \right) \]

Where:

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.

Example Calculation

Let's assume the following values:

Using the formula:

\[ d = \sqrt{(3 - 0)^2 + (4 - 0)^2} = \sqrt{9 + 16} = 5 \]

\[ (x, y) = \left( 0 + \frac{5 \times (4 - 0)}{5}, 0 + \frac{5 \times (0 - 3)}{5} \right) = (4, -3) \]

The point of tangency is (4, -3).