Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.
Let, triangle ABC be a right angle triangle at ∠B
Let P be the mid-point of hypotenuse AC
Draw a circle with centre P and AC as diameter
Since,
∠ABC = 90o
Therefore, the circle passes through B
Therefore,
BP = Radius
Also,
AP = CP = Radius
Therefore,
AP = BP = CP
Hence, BP = AC