5

Part of 1964 German National Olympiad

Problems(1)

<C= ? if <B=45^o and BP : PC =1 : 2, APC = 60^o , without trigonometry

Source: 1963-64 Germany R4 12.5 https://artofproblemsolving.com/community/c3208025_

ABC

\beta= 45^o

is given. There is a point

P

BC

BP : PC =1 : 2

(inner division) and

\angle APC = 60^o

. Someone claims that you can do it with elementary geometric theorems alone without using the plane trigonometry, the size of the angle

\gamma