In an equilateral triangle , is a point on side such that , Prove that .
Step-1:Construction:
Draw altitude perpendicular to
Step-2: Express in terms of :
Consider right angled with right angle at vertex .
By applying Pythagoras theorem
In an equilateral triangle, the altitude bisects the opposite side i.e.
Step-3: Express in terms of :
Consider right angled with right angle at vertex .
By applying Pythagoras theorem
From the figure we know that
Step-4: Substitute the obtained values to prove the required result:
Substituting and in we get,
Dividing throughout by we get
Hence,it is proved that .