SOLUTION: Prove: The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices. A(0.0) B(a,0) C(0,b)

Question 426510: Prove: The midpoint of the hypotenuse of a right triangle is equidistant from the three vertices.
A(0.0) B(a,0) C(0,b)
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
The midpoint of the hypotenuse BC is (, ). We can find the distance from each point to the midpoint and show that they are all equal.

A better way to prove this is to circumscribe a circle around ABC. Since BAC is a right angle, the hypotenuse BC is a diameter of the circle. We can draw the midpoint D and show that DA, DB, DC are all radii of the circle, hence they are equal.
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