# Thread: Right Triangle Circumscribed Circle Proof

1. ## Right Triangle Circumscribed Circle Proof

Prove that the hypotenuse of a Euclidean right triangle is a diameter of the circumscribed circle.

Given theorem: Let $\displaystyle \triangle{ABC}$ be a triangle and let M be the midpoint of segment AB. If $\displaystyle \angle{ACB}$ is a right angle, then AM = MC.

I've drawn a diagram to help me but don't know where to begin on the proof.

2. ## I think I've got it

I think I finally figured out how to do this.

No help needed - THANKS!!!

3. Originally Posted by ReneePatt
Prove that the hypotenuse of a Euclidean right triangle is a diameter of the circumscribed circle.

Given theorem: Let $\displaystyle \triangle{ABC}$ be a triangle and let M be the midpoint of segment AB. If $\displaystyle \angle{ACB}$ is a right angle, then AM = MC.

I've drawn a diagram to help me but don't know where to begin on the proof.

there is a theorem that said
the circum angle established on the diameter equal 90 you can use this theorem

and the converse of it is true the angle established on the diameter from the circum of the circle equal 90

,

### triangle LGC is a right triangle with rt.angle LCG and M is the midpoint of LG prove that MC=½LG

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