[SOLVED] Trig chord angle problem
This should be simple but its got me stumped so I could use some help.
: *** :
: ** + : : is the tangent line
: +\* : + marks the line in question
: + \ * : \ marks the chord line
: + \ *: - marks the radius line
: + \ *
: + \* circle
I have a circle of radius r. A line at 0degrees is drawn from the center to the circle edge. At the point of intersection a tangent line can be drawn. There is a chord line of known length (ra) that bisects the line between the radius line and the tangent line. Since the radius of the circle is known and the length of the chord line is know how can I calculate either the angle theta (angle between the two lines) or the angle of the chord line or the x and y point where the chord line (re)crosses the circle. sorry the drawing is so bad... hard to do with ascii art ;)
A simple metaphor is this: You grab a slice of pizza. You have a tape measure and measure the length of the side of the piece and you measure across the widest point at the top of the piece - remember the second width is not the arc length as you just measured the straight distance across the piece. Given these two how do you determine the angle of the piece, or the angle of incident between one side and the straight line that connects the two end points of the piece.
thx in advance