Math help???? PLEASE should be fairly simple?

Question

I have 2 questions i just can not get. Please help me in any way you can, being as descriptive as you can while still speaking simply (please explain the terms you use.)

first, there is:

Use you knowledge of circle theorems to proove that you have produced an incirle and a circumcircle. THIS pretty much says proove that you have made a triangle inside a circle, and a circle inside a triangle. Now i know you can't see that picture, bu anyone know how i can proove it?

And there is also:

Prove that for all right angle triangles that the midpoint of the hypotenuse is always the circumcentre of the circumcircle.

Help please?

Answer 1

I started to answer this before and quit because I'm not sure I can give you much help.  Since you ask again, though:

On your first problem, we'd have to know how you produced the incircle and circumcircle before we could even begin to answer it.

On the second, it would be sufficient to show that the midpoint of the hypotenuse is equidistant from all three vertices of the triangle.  Since it's the midpoint of the hypotenuse, it's pretty much a two-step proof to show that it's equidistant from the ends of the hypotenuse.  Showing it to be equidistant from the third vertex is harder, and I'm afraid that's where I'm going to fail you because I don't see an easy way right off the bat.  I'd suggest you take this germ of an idea and dig back into your textbook.  There's probably a specific postulate or theorem that will give you the key to it.

Sorry not to be more help, but at least you have an answer.  :)