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OlympiadHardGeometry10–12

A point $P$ inside an equilateral triangle $ABC$ satisfies $PA = 3$ , $PB = 4$ and $PC = 5$ . How many degrees does angle $APB$ measure?

Um ponto $P$ no interior de um triângulo equilátero $ABC$ satisfaz $PA = 3$ , $PB = 4$ e $PC = 5$ . Quantos graus mede o ângulo $APB$ ?

Answer options

Solution

Step 1 of 3

1.Rotate the triangle $60^\circ$ about $B$ , sending $A$ to $C$ and $P$ to $P'$ .