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).

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