IMO Shortlist 1979 problem 17
Dodao/la:
arhiva2. travnja 2012. Inside an equilateral triangle
![ABC](/media/m/a/c/7/ac75dca5ddb22ad70f492e2e0a153f95.png)
one constructs points
![P, Q](/media/m/9/d/a/9da751d159f7958b2dce8836cab49820.png)
and
![R](/media/m/4/d/7/4d76ce566584cfe8ff88e5f3e8b8e823.png)
such that
![\angle QAB = \angle PBA = 15^\circ,\\ \angle RBC = \angle QCB = 20^\circ,\\ \angle PCA = \angle RAC = 25^\circ.](/media/m/9/f/7/9f7b4942965879fc6e49f18de338e74a.png)
Determine the angles of triangle
%V0
Inside an equilateral triangle $ABC$ one constructs points $P, Q$ and $R$ such that
$$\angle QAB = \angle PBA = 15^\circ,\\ \angle RBC = \angle QCB = 20^\circ,\\ \angle PCA = \angle RAC = 25^\circ.$$
Determine the angles of triangle $PQR.$
Izvor: Međunarodna matematička olimpijada, shortlist 1979