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.

Let $A(0,0)$, $B(2,0)$, $C(c_{x}, x_{y})$, $D(d_{x}, d_{y})$.
$O_1$ and $N$ is the center of circles (ABD) and (CKL).
Find coordinates of $C, N, K, L, O_1$.![Don't take care about coordinate system in picture - wrong numbers!][1]

share|improve this question
    
Typo: $B=(4,0)$. You can determine $O_1$ using the fact that it is equidistant of $A,B,D$. So it is the intersection of the 2 mediatrix, and of course, it will be in function of $d_x,d_y$. –  Sigur Sep 6 '12 at 22:34
    
There seems to be a lot of unstated information. For example, is $d_y=2$? Is this a parallelogram? –  Henry Sep 6 '12 at 22:50
add comment

1 Answer

up vote 1 down vote accepted

Hints:

  • $O_1$ is on the perpendicular bisectors of $AB$ and $AD$, so for example its $x$-coordinate is $2$.

  • $N$ is twice as far away from $A$ as $O_1$, in the same direction.

  • If this is a parallelogram, the coordinates of $C$ are the sum of the coordinates of $B$ and $D$.

  • When calculating the coordinates of $L$ and $K$ you will have to solve quadratic equations, with two solutions, one of which gives $C$.

share|improve this answer
add comment

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.