Question

9. In a ∆ABC, ID, IE and IF are the perpendicular bisectors of BC, AC and AB respectively. Prove that
I is equidistant from the vertices of the triangle.​

Answer 1

Step-by-step explanation:

You will need to draw an accurate figure to see this clearly.

 

Draw the ⊥ bisector of 2 sides of the triangle which will meet in a point (because they are ⊥ to non-parallel lines).  The point may or may not be inside the triangle.

 

From this intersection (I in your problem), construct lines to each vertex of the triangle.  These lines are of equal length:

AI = BI because the intersection lies on the perpendicular bisector of AB; similarly BI = CI because the intersection lies on the perpendicular bisector of  BC.  Then AI = CI.  QED