Tangent Line to a Circle

An equation of the form [math]r\cos\left(\theta-\alpha\right)=d[/math] describes a line tangent to the circle [math]r=d[/math] at the point [math]\left(d,\alpha\right)[/math].[br][br]Drag the sliders for [math]d[/math] and [math]\alpha[/math] to see how the graph and equation change. You can show or hide the circle that the line is tangent to as well as the radius to the point of tangency.[br][br]To see where this equation comes from, show the "Point on the Line." Be sure to have the radius showing as well.[br][br]Notice the radius and the segment to the point form a right triangle, which leads to the relationship:[br][math]\cos\left(\theta-\alpha\right)=\frac{d}{r}[/math][br][br]Multiplying both sides by [math]r[/math], we get:[br][math]r\cos\left(\theta-\alpha\right)=d[/math]

Information: Tangent Line to a Circle