Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

We know the values of the coordinates (Xa,Ya), (Xb,Yb), and (Xc,Yc). We also know the lengths of A, B, and C. Is there a way (equation) to figure out the exact coordinates where the three lines A, B, and C intersect (the x? and y?).

I assume you could rotate all three of the lines until eventually they matched up.

enter image description here

share|cite|improve this question
up vote 1 down vote accepted

Yes. The point $(x,y)$ you want is on the following three circles :

$$C_a : (x-X_a)^2+(y-Y_a)^2={r_a}^2$$ $$C_b : (x-X_b)^2+(y-Y_b)^2={r_b}^2$$ $$C_c : (x-X_c)^2+(y-Y_c)^2={r_c}^2$$ where $r_a,r_b,r_c$ represents the lenght of $A,B,C$ respectively.

$C_a$ and $C_b$ have two intersection points at most. So, You can get the coordinate using the equation of $C_c$.

share|cite|improve this answer
Thanks, its going to take me a minute to process it all and work it out in actual equating haha. – Michael-R Jan 3 '14 at 5:06
You are welcome! – mathlove Jan 3 '14 at 5:07

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.