Question

Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half the hypotenuse.

Answer 1

We have to prove that  ` BP = 1/2 AC`

Let   Δ ABC  be a right angle at B and P be midpoint of AC

Draw a circle with center at P and AC diameter

Since ` angle ABC = ` 90°   therefore circle passing through B

So  `BP = CP = `radius

`⇒ AP = BP = CP `

Hence

`BP = 1/2 AC` Proved.