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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 -

We have to prove that  
 
Let   be a right angle at B and P be midpoint of AC
Draw a circle with center at P and AC diameter
Since   therefore circle passing through B
So  
 
Hence 
 Proved.

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