Thread: guadrilateral inscribed in a circle...

If a quadrilateral ABCD is inscribed in a circle, then the opposite angles of the quadrilateral are supplementary.

I'm not sure how to write this proof. Any help would be greatly appreciated!

Originally Posted by mdk

If a quadrilateral ABCD is inscribed in a circle, then the opposite angles of the quadrilateral are supplementary.

I'm not sure how to write this proof. Any help would be greatly appreciated!

Sorry, I labelled the angles the same as your vertices.
This was not intentional.

Join all corners of the quadrilateral to the circle centre "o".
you now have 4 isosceles triangles with the angles at the circumference within each triangle equal.

Therefore 2A+2B+2C+2D =360 degrees.
A+B+C+D=180 degrees.

(A+B)+(C+D)=180 degrees.
(A+C)+(B+D)=180 degrees.

Thank you so much for the help and the picture. It really helps to see it.
mdk