How To Prove The Intersecting Chords Theorem Of Euclid

P is typically in the middle of the circle, but slightly off-center. Both the A,B line and the C,D line will intersect that point.

You can either measure all the angles by hand, or you can use the vertical angles theorem (when two straight lines intersect, they form two sets of linear pairs with congruent angles) to prove that ABP and CDP are the same. Then, you can use the inscribed angle theorem (an angle inscribed in a circle is half of the central angle that is on the same arc on the circle) to prove that angle A and angle C are equal. Finally, use the inscribed angle theorem again to prove that angle B and angle D are equal.