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Question Number 207362 by mr W last updated on 12/May/24

	Answered by A5T last updated on 12/May/24

	${P t o l e m y}^{'} s t h e o r e m : A C \times B P = A P \times B C + A B \times P C$ $A B = A C = B C \Rightarrow P B = P A + P C$
	Answered by sniper237 last updated on 13/May/24

	$L e t Q \in [B P] s u c h a s P Q = P C$ $A s m e s B P C = m e s B A C = 60 t h e n$ $Q P C i s e q u i l a t e r a l a s A B C$ $S o r (A) = B a n d r (P) = Q w i t h r = R (C; \frac{π}{3})$ $T h u s r i s a n i s o m e t r y, P A = B Q$ $T h e n P B = P Q + Q B = P C + P A$
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