.geometry "version 0.51";
.l0; 
.text("Construct \triangleABC given BC and the
lengths of the altitudes from B and C.  Test
the diagram by modifying the lengths of
BC, h\sub{B} and h\sub{C}.", .l0);
v1 = .free(-0.904192, 0.835329);
v2 = .free(-0.185629, 0.832335);
v3 = .free(-0.898204, 0.727545);
v4 = .free(-0.206587, 0.727545);
v5 = .free(-0.904192, 0.583832);
v6 = .free(-0.326347, 0.586826);
l1 = .l.vv(v1, v2, "BC");
l2 = .l.vv(v3, v4, "h\sub{B}");
l3 = .l.vv(v5, v6, "h\sub{C}");
v7 = .free(-0.242515, -0.158683, "B");
c1 = .c.ctrvv(v7, v1, v2, .in);
v8 = .vonc(c1, 0.476048, -0.161793, "C");
l4 = .l.vv(v7, v8, [.white, .blink, .white]);
c2 = .c.ctrvv(v7, v3, v4, [2 .in, .blink, .white, 2 .in, .white]);
l5 = .l.vc(v8, c2, 1, [3 .in, .blink, .white, .in, .white], .longline);
c3 = .c.ctrvv(v8, v5, v6, [4 .in, .blink, .in, .white]);
l6 = .l.vc(v7, c3, 2, [4 .in, .blink, .in, .white], .longline);
v9 = .v.lc(l5, c2, 2, [.white, 2 .in, .white]);
v10 = .v.lc(l6, c3, 2, [.white, 3 .in, .white]);
v11 = .v.ll(l6, l5, [.white, 4 .in, .blink, .white], "A");
v12 = .v.ll(l4, l5);
l7 = .l.vv(v7, v9, [.white, 2 .in, .white], "h\sub{B}");
l8 = .l.vv(v8, v10, [.white, 3 .in, .white], "h\sub{C}");
l9 = .l.vv(v7, v11, [.white, 3 .in, .white]);
l10 = .l.vv(v11, v8, [.white, 2 .in, .white]);
.text("Construct a segment of length BC.", .l1);
.text("Draw a circle of radius h\sub{B} around point B.
The foot of the altitude must lie on this circle.", .l2);
.text("Draw a tangent to the circle from point C.
this is the only point where the altitude will be
perpendicular to the line CA.", .l3);
.text("Similarly, draw a circle of length h\sub{C}
around C and find the tangent to this
circle from B.", .l4);
.text("Let A be the intersetion of these two
tangent lines.", .l5);
.text("Press 'Next' to continue ...", .red, .tol5);