Question

RM and CN are perpendiculars to a line passing through the vertex A of a triangle ABC. IF L is the mid-point of BC, prove that LM = LN.

Answer 1

In BM and CN are perpendiculars on any line passing through A.

Also.

We need to prove that

From point L let us draw

It is given that , and

Therefore,

Since, L is the mid points of BC,

Therefore intercepts made by these parallel lines on MN will also be equal

Thus,

Now in ,

And . Thus, perpendicular bisects the opposite sides.

Therefore, is isosceles.

Hence

Hence proved.