Thread: Prove that trapezoid inscribed in a circle is isosceles.

Prove that trapezoid inscribed in a circle is isosceles?
I have a trapezoid ABCD ...dont know how to prove digonals AC = BD? Help...

Originally Posted by winsome

Prove that trapezoid inscribed in a circle is isosceles?
I have a trapezoid ABCD ...dont know how to prove digonals AC = BD? Help...

Draw lines from the center of thecircle to each vertex. consider the triangles formed and use the fact that the sides from the center to the vertices are all congruent. You will probably need to consider two cases: where the center of the circle is inside the trapezoid and where it isn't.

Hello, winsome!

Is it really this simple?

Prove that trapezoid inscribed in a circle is isosceles.

Code:

              * * *
        A o-----------o B
        */             \*
       */               \*
       /                 \
    D o-------------------o C
      *                   *
      *                   *

       *                 *
        *               *
          *           *
              * * *

Originally Posted by Soroban

Hello, winsome!

Is it really this simple?

Code:

              * * *
        A o-----------o B
        */             \*
       */               \*
       /                 \
    D o-------------------o C
      *                   *
      *                   *

       *                 *
        *               *
          *           *
              * * *

Thanx for Reply but i have few more issues,
is there another solution if we not consider the property of Parallel lines intercept equal arcs ?as i need the solution without using this property.