In Fig.1 given that DE, DF & DG are respective perpendiculars to AB, AC & BC
Prove that E, F & G are collinear.
(I found this problem on youtube but on trying to solve through co-ordinate geometry, the expression becomes very complex after a few steps, is there any elegant solution!)
In Fig.2 given that EC & ED are tangents to the semicircle
Prove that EO is perpendicular to AB.
(I found this problem on twitter and was able to solve it through co-ordinate geometry but the steps were too long and complex. There should be an elegant solution)