practice problems
Q1. S1. Problem involving triangle and altitudes => look for cyclic quadrilaterals. B,C,E,F are concyclic. Why? Since BC is a diameter and F,E inscribe 90 deg at circumference. In a cyclic quadrilateral, exterior angle at a vertex is equal to the interior angle at the opposite vertex. So, angle AFE = angle BCE since AFE is the exterior angle at F and C is the opposite interior angle. Similarly angle AEF = angle CBF Now in triangles ABC and AEF all the angles are equal. Hence ABC ~ AEF (Note the ordering of vertices).