I am driving a boat in the sea at S. When I measure the angles ASB = and BSC = and CSA, they are 100, 125 and 135 respectively.
a) Could you simply use compass, protractor and straightedge to locate where I am?
(Hint: Angle at center twice the angle at circumference)
b) By keeping A, B, C unchanged, try to adjust and so that my location is outside the triangle ABC. Could you use the method used in a) to locate where I am?
c) Could you find some combinations of and , so that the solution is infeasible?
d) Try to move B so that B is between A and C anti-clockwisely. Is this method also applied?
e) The circumcircle of triangle ABC is called "danger circle". Could you find a combination of positions A, B, C and angles and , so that S is located at the "danger circle"? Could you explain why such circle is so dangerous?