Proving a triangle in a circle is degenerate

How do I prove that a triangle inscribed in a circle (where all 3 sides are touching the circumference of the circle) is degenerate when above 135 degrees?

Just a part of a problem im working on and im nearly there but i need to prove this part

Cheers

Re: Proving a triangle in a circle is degenerate

Quote:

Originally Posted by

**pikachu26134** How do I prove that a triangle inscribed in a circle (where all 3 sides are touching the circumference of the circle) is degenerate when above 135 degrees?

Just a part of a problem im working on and im nearly there but i need to prove this part

Cheers

No this is not true. You have posted a problem where the things are different, i was not trying to say that any triangle having one of its angles as 135 deg is degenerate. You can circumscribe any triangle by a circle. A 135,22.5,22.5 triangle is of course non degenerate. Circumscribing it wouldn't *make* it degenerate!!!

Re: Proving a triangle in a circle is degenerate

Hello, pikachu26134!

Perhaps if you give us the original problem,

. . your question will make sense.

Quote:

How do I prove that a triangle inscribed in a circle

(where all 3 sides are touching the circumference of the circle)

is degenerate when above 135 degrees?

You say that the triangle is **inscribed** in a circle.

. . (The triangle is *inside* the circle; the *vertices* touch the circle.)

Yet you say the **sides** are touching the circle.

. . Perhaps you mean "a circle is inscribed in a triangle"?

Also, *what* is above 135 degrees?

You begin with "We have a triangle."

Then add that it has either an incircle or a circumcircle.

Then (I think) make one angle greater than 135 degrees.

And now *we don't have a triangle ?*

. . (It shrinks to a point?)