| Statement | Reason |
|---|---|
| Triangle ABD is inscribed in the circle with center at C. | Construction |
| AC, BC, and DC are all length 1 | They are all radii of the circle |
| If we continue DC until it intersects AB at E, the two lines meet at right angles | Since the triangle is equilateral, DC bisects angle ADB and so the two angles at E are equivalent and add up to 180 degrees (*) |
| Angle CAE is 30 degress | AC bisects angle DAB |
| AE is length sqrt(3)/2 | It's part of a 30-60-90 right triangle |
| AD is length sqrt(3) | AD is twice the length of AE |
(*) - I left out a few steps from a completely formal proof, but you get the idea here