circle geo (1 Viewer)

[Joshmosh2]

Two chords AB and CD intersect within a circle at X. Prove that angle AXC is equal to the sum of the angles subtended at the circumference by the minor arcs AC and BD.

 

[aDimitri]

By constructing lines AD & CB, we get the ever-so familiar butterfly shape. The angle from the minor arc AC is ACD, & the angle from the minor arc BD is BAD. Since the exterior angle of a triangle is equal to the sum of the two opposite interior angles, AXC = ACD + BAD
It's not a theorem, but it's a fairly short question