Q. In the given triangle ABC, AD is perpendicular to BC, and CE is perpendicular to AB. Prove that angle BDE = angle BAC.

Soln:

i) ACDE is a cyclic quadrilateral. 

i) ÐAEC = ÐADC = 90 degree (Angles in the same segment of a circle are equal.)

ii) ÐBDE = ÐCAE                      

ii) Exterior angle of cyclic quadrilateral is equal to its opposite interior angle