Q28 of 100 Page 17

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


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