Geometry · Angle chasing · Circumcenter · Inscribed angle theorem · Cyclic quadrilaterals · Isosceles triangles
In triangle \(ABC\) the angles at \(A\) and \(B\) measure \(\angle A = 50^\circ\) and \(\angle B = 60^\circ\). Points \(D\) and \(E\) are taken on the sides \(AB\) and \(BC\) respectively, so that
\[ \angle DCA = \angle EAC = 30^\circ . \]
Determine \(\angle CDE\).
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Serbian Regional Competition (Okruzno takmicenje) 1998, high school grade I, problem 5. The 1998 regional paper was not split into categories. Organized by the Mathematical Society of Serbia (DMS). Source