Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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|improve this question

1 Answer 1

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

Your Answer

 
discard

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.