Originally posted by phgao
Alice's netball squad warms up by spacing themselves equally around a circle, facing inwards, and doing the following exercises.
In the first exercise, each girl passes the ball to the first player on her left, starting and ending with Al ...[text shortened]... layers required, and which exercise uses an angle of 17.5 degrees?
OK, got the proof.
Draw the circle and the 9 girls (g1, g2, etc) equally spaced around it. Draw in the center point C.
If the ball is passed 4 to the left twice, it will end up at the girl 1 right (g9). The angle from the center to g1 and g9 is 360 degrees divided by 9, or 40 degrees.
Now draw a diameter from the second girl (the vertex of the unknown angle, or g5) to the point midway between g1 and g9 through the center (m). Now we can describe a triangle Cmg1. Angle g1Cm is half of 40 degrees, or 20 degrees.
Angle g1Cg5 is 180 degrees minus angle g1Cm, or 160 degrees.
Triangle g1Cg5 is an isoscoles triangle (is that the right word? It has two sides the same and one different). The "different" angle is g1Cg5 = 160 degrees. The other two must be identical, and must sum up with 160 degrees to make 180 degrees; so each is ten degrees.
So, angle g1g5m is ten degrees. But m is midway around the circle from g1 to g9; clearly angle mg5g9 is also ten degrees. Sum these two and you get angle g1g5g9, which is twenty degrees.
Did I make that clear and rigorous enough?