# Proving a triangle in a circle is degenerate

• Jul 5th 2011, 05:41 PM
pikachu26134
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
• Jul 5th 2011, 08:12 PM
abhishekkgp
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!!!
• Jul 6th 2011, 04:05 AM
Soroban
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?)