# Thread: Length of Equal Tangents

1. ## Length of Equal Tangents

Two circles of radii 5 cm and 8 cm touch externally. Calculate the length of the common tangent.

Here Ive attempted it, creating two simultaneous equations for the external point and the centers of each circle. From there i attempted the cosine rule, but to no avail.

Thanks for help.

2. Draw a picture of the circles and the tangent. You should be able to form a right-angled triangle, use pythatogra's thm to solve for the tangent (longest side).

3. I actually did that the first time. But in using pythagoras, ive got 2 variables each from one circle. So i cannot solve. Unless you can point it out to me on the diagram ill post now.

4. Your picture is not what I had imagined the question to be. Do you know if what you have posted is correct?

My intepretation was a line that went from the top of one circle to the other. I think the word 'common' is misleading here.

5. Yes i see what you mean. Thanks for your correction. But just interested is there a way of doing such a question, like the one given in the diagram?

6. Hello Lukybear
Originally Posted by Lukybear
Yes i see what you mean. Thanks for your correction. But just interested is there a way of doing such a question, like the one given in the diagram?
No. Take a look at the diagram I've attached - which is a modified version of yours.

You'll see that the point where the tangents meet can be anywhere along the vertical line. I've marked the original position as $\displaystyle P_1$ and shown a second possible position, $\displaystyle P_2$.