## Interior Tangent to Two Circles

**How to construct a tangent that goes between two circles**

**What You Start With**

Shown above are two circles of different radius.

**Interior Tangent to two Circles**

- This can be a tricky question but if you think about it, it is actually quite easy. We have already covered a tangent to a circle from a point outside the circle. This question is is based on the principles of that question if you relax the constraints of the two circles to suit what we already know on a tangent from a point outside a circle.
- What I mean by that is if shrink the smaller circle until it is just a point, you can apply the same principles from a tangent to a point outside a circle. The only thing to remember is that since you want the tangent to go between the two circles, if you decrease the radius of one circle until it is a point you increase the second circle by the same distance.
- Once you have a point (point C)and a larger circle ( represented by the red red arc) then you can apply what you have already learned on tangent to a point outside a circle.

- First we join point B to the centre of the circle A and bisect this line.
- Where the perpendicular bisector, bisects line AB gives us point E. Take the radius AE and swing from point E. This will cut the red circle at point F. We know that the tangent is the line drawn from the point B through that point F, however since we relaxed the constraints of the question we must not re-introduce them to it.
- As we increase the point B back to its original radius we also decrease the larger circle back to its original size.
- We stop when the circles reach their original size and that is the interior tangent of the two circles.

- The point of contact for the big circle can be located by joining point F to point A and where that line cuts the circle give you the point of contact. (Point G)
- The second point of contact can be located by drawing a line parallel to line FA from the center of the circle B until it hits the circle at point H.

Interior Tangent to two Circles Interactive