Prove that if you draw a right triangle and then draw a circle with its center on the hypotenuse's midpoint such that it intersects at least 1 vertex, it will in fact intersect all three.

Since the centre of the circle lies on the mid-point of the hypotenuse, each of the two halves is the radii, hence the circle will pass through them definitely.

For the third point, the one having the right angle, it is known that the angle in a semi-circle is 90 degrees and vice-versa, i.e. if a chord subtends 90 degree angle at any other point, the circle must pass through that point.

Hence, proved.

Posted by shawn on 2004-02-24 11:26:10