Tangent-Radius Theorem

• • If a tangent line, a radius, and a circle all intersect at the same point, the tangent line and the radius will be perpendicular

Again, a picture makes this easier to understand

You can see that the tangent line and the radius meet at a 90° angle on the circle.

Does it matter where they intersect on the circle? I decided to check it out using GeoGebra

As you can see, no matter where I try along the circle, the tangent line and the radius always meet at a right angle.

Hopefully you can just imagine this video if you ever need to remember. Euclid also proved it if you'd like to check out his proof here.