Ladies and Gentlemen:

In the course of my CFD work, I've come upon a problem which at first seems nearly trivial, but which, I'm embarassed to say, I haven't solved. Perhaps someone can help.

- Consider two line segments of known length.

- They are connected together, non-parallel, and the angle they form is known.

- Now without disturbing their geometry, consider those two segments as two adjacent, connected chords of a circle.

What is the radius of the circle which circumscribes the two segments as valid chords?

Thanks in advance.

if one side has length a and the second has length c, and the line connecting the two extremes (to make a triangle) has length b, then the radius R of the circle is

R = a.b.c / (4.D)

where D = sqrt( s.(s-a).(s-b).(s-c) )

and s = ( a + b + c ) /2

adrin

Thank you for replying:

In my problem, we don't know the length b. But we do know the angle, phi, that is formed by the vertex of the two line segments.

Any ideas?

Rich

If you know the end points of the two line segments a and c, then you know the length b, regardless of the angle, do you not?

The length c, for known lengths a and b, and the angle C between them is given by the law of cosines:

c^2 = a^2 + b^2 - 2.a.b.Cos(C)

adrin

We don't know the endpoints. We only know the lengths of the two line segments and the included angle.

Rich

Ah, thanks!

i need trigonometry puzzles for my project in mathIV. . . please give me a trigonometry puzzles. . .