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