Online Geometry Problem 835: Isosceles Triangle, Double Angle, Triple Angle, Auxiliary Lines. Level: High School, SAT Prep, College, Mathematics Education

The figure below shows an isosceles triangle ABC (AC = BC). Angle CAD = 2 angle CBD and angle ACD = 3 angle BCD. Find the measure of angle BDC. Try to use elementary geometry (Euclid's Elements).