This document contains two proofs about angles in circles: 1) It proves that the angle at the center of a circle is twice the size of the angle at the circumference when intersected by the same arcs. It does this by showing two isosceles triangles have equal base angles. 2) It proves the same relationship between the angle at the center and circumference by considering two angles formed by chords and an angle in the circle. It sets up an equation relating the angles and solves it to show the center angle is twice the circumference angle.