Tangents to a Circle

Circle showing a tangent line touching at one point and other intersecting lines

A tangent is a line that touches a circle at exactly one point.

That point is called the point of tangency.

The Radius is Perpendicular

A very important rule is that the radius to the point of tangency is always perpendicular (at right angles) to the tangent line.

Circle with a tangent line and radius meeting at a right angle

This means the angle between them is always 90°.

Try it: Draw a circle, and its radius, and then use a protractor to draw a line at 90°. That line will be a tangent!

When we draw two tangent lines from the same outside point to a circle:

Two tangent lines from a single outside point showing equal lengths and angles

When we have two circles, we can draw lines that are tangent to both of them at the same time. These are called Common Tangents.

Two circles with their external and internal common tangents

These stay on "the outside" and don't cross the space between the circles.

These cross through the space between the two circles.

We can also have these cases:

Circles just touch, outside

Circles intersect

Circles just touch, inside

Circle inside circle

Now you know the first secrets of the tangent!