File:Sehne.svg

// created with Asymptote 2.67: The Vector Graphics Language
// using online-editor: http://asymptote.ualberta.ca/

import graph;

size(175);

/* given values */
pair M = (0,0);    // center
real r = 1;        // radius

real angleA  = 100;    // angle of point A [°]
real angleB  = 350;    // angle of point B [°]
real angleC1 =  20;    // angle of point C1 [°]
real angleC2 =  50;    // angle of point C2 [°]
real angleC3 = 185;    // angle of point C3 [°]
real angleC4 = 225;    // angle of point C4 [°]

// returns a pair representing a point on a circle with center c and radius r at angle degrees
pair pointOnCircle(pair c = (0,0), real r = 1, real degrees = 0) {
    return c + scale(r) * dir(degrees);
}

// returns an arc with radius r centered at c from pair z1 to z2
path arc(pair c, pair z1, pair z2, real r, bool direction=CCW) {
    return arc(c, r, degrees(z1 - c), degrees(z2 - c), direction);
}

// returns an arc with radius r centered at c from pair z1 to z2
//path Arc(pair c, pair z1, pair z2, real r, bool direction=CCW, int n=nCircle) {
//    return Arc(c, r, degrees(z1 - c), degrees(z2 - c), direction, n);
//}

pair A  = pointOnCircle(M, r, angleA);     // calculate position of point A
pair B  = pointOnCircle(M, r, angleB);     // calculate position of point B
pair C1 = pointOnCircle(M, r, angleC1);    // calculate position of point C1
pair C2 = pointOnCircle(M, r, angleC2);    // calculate position of point C2
pair C3 = pointOnCircle(M, r, angleC3);    // calculate position of point C3
pair C4 = pointOnCircle(M, r, angleC4);    // calculate position of point C4

draw(arc(M, r, angleA, angleB, CW), heavygreen);     // draw arc b1 from A to B
draw(arc(M, r, angleA, angleB, CCW));                // draw arc b2 from A to B
draw(A--B, yellow+linewidth(1.5));                   // draw background of chord
draw("$s$", A--B, red);                              // draw chord s from A to B
label("$k$", pointOnCircle(M, r, -45), dir(-45));    // label circle

// draw radius and angle at M
draw("$r$", M--A, heavygreen);
draw("$r$", B--M, heavygreen);
draw("$\alpha$", arc(M, A, B, 0.25 * r, CW), heavygreen);

// draw angle at C2
draw(C2--A, blue);
draw(C2--B, blue);
draw("$\varphi$", arc(C2, B, A, 0.25 * r, CW), blue);
//draw(shift(2,0) * Label("$\varphi$", Relative(0.2)), arc(C2, A, B, 0.1 * r), blue);

// draw angle at C1
draw(C1--A, blue);
draw(C1--B, blue);
draw(Label("$\varphi$", UnFill), arc(C1, B, A, 0.25 * r, CW), blue);
//draw("$\varphi$", arc(C1, A, B, 0.1 * r), blue);

// draw angle at C3
draw(C3--A, magenta);
draw(C3--B, magenta);
draw("$\psi$", arc(C3, A, B, 0.35 * r, CW), magenta);

// draw angle at C4
draw(C4--A, magenta);
draw(C4--B, magenta);
draw("$\psi$", arc(C4, A, B, 0.35 * r, CW), magenta);

dot(M);     label("$M$", M, W);                  // draw center M
dot(A);     label("$A$", A, dir(angleA));        // draw point A
dot(B);     label("$B$", B, dir(angleB));        // draw point B
dot(C1);    label("$C_1$", C1, dir(angleC1));    // draw point C1
dot(C2);    label("$C_2$", C2, dir(angleC2));    // draw point C2
dot(C3);    label("$C_3$", C3, dir(angleC3));    // draw point C3
dot(C4);    label("$C_4$", C4, dir(angleC4));    // draw point C4

draw(Label("$b_1$", Center, UnFill), arc(M, 1.15 * r, 60, 90), heavygreen, Arrows);    // label arc b1
draw(Label("$b_2$", Center, UnFill), arc(M, 1.15 * r, 125, 160), Arrows);              // label arc b2