Question

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.

Answer 1

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 = 90° 

Therefore, 

the circle passes through B 

Therefore, 

BP = Radius 

Also, 

AP = CP = Radius 

Therefore, 

AP = BP = CP 

Hence, 

BP =  \(\frac{1}{2}\)AC