Let A B C be an acute-angled triangle and P be a point in its interior. Let P_A, P_B , and P_C be the images of P under reflection in the sides B C, C A and A B , respectively. If P is the orthocentre of the triangle P_A P_B P_C and if the largest angle of the triangle that can be formed by the line segments P A , P B , and P C is x^ ; determine the value of x .

Step-by-step solution

A B is bisector P P_C & A C is bisector of P P_B . A is point of intersection of bisectors A is circumcentre of P P_B P_C Circumradius =C R ( P P_B P_C )=P A Similarly, C R ( P P_C P_A )=P B & C R ( P P_A P_B )=P C But C R ( P P_A P_B )=C R ( P P_B P_C )=C R ( P P_C P_A )= C R ( P_A P_B P_C )P C=P A=P B=C R ( P_A P_B P_C )P A=P C Required triangle is equilateral triangle x=60^