# Circle and three lines

• October 4th 2008, 05:39 PM
joesmith13610
Circle and three lines
Hello everyone I am new to the forums. I didnt know where to put this one, either in the high school or college section.

I was wondering if you guys/gals can help me out with this problem.
I dont really know how to start the problem.

here you go:

We are given three infinite straight lines. we need to construct a circle that touches the first two lines and has its center on the third line?

Any help is appreciated.

thanks everyone

joe
• October 4th 2008, 06:35 PM
Jhevon
Quote:

Originally Posted by joesmith13610
Hello everyone I am new to the forums. I didnt know where to put this one, either in the high school or college section.

I was wondering if you guys/gals can help me out with this problem.
I dont really know how to start the problem.

here you go:

We are given three infinite straight lines. we need to construct a circle that touches the first two lines and has its center on the third line?

Any help is appreciated.

thanks everyone

joe

what do we know about the lines? are they parallel, perpendicular, skew? was that all the info you were given?
• October 4th 2008, 07:12 PM
Soroban
Hello, Joe!

Welcome aboard!

Quote:

We are given three infinite straight lines.
We need to construct a circle that is tangent to the first two lines
and has its center on the third line.

Code:

```              L2 /                  /                 /                  /                 /                  ♥ C               /                o /               /              o  /             /            o    /             /          o      /           /        o        / L3           /      o          /         /    o            /         /  o              / L1    / o                /   - - * - - - - - - - - - * - - - - - -     /                  /     /                  /```
Assuming that the lines intersect . . .

Construct the bisector of the angle formed by $L_1$ and $L_2.$
. . The center of our circle lies on this angle bisector.

Locate the intersection $C$ of the angle bisector and $L_3.$
. . $C$ is the center of the circle

Determine the perpendicular distance from $C$ to $L_1$ (or to $L_2$).
. . That is the radius of the circle.

• October 4th 2008, 08:13 PM
joesmith13610
Quote:

Originally Posted by Jhevon
what do we know about the lines? are they parallel, perpendicular, skew? was that all the info you were given?

that was all the info we got.

joe