Ancient Greek mathematician Thales of Miletus is given credit for this theorem. My professor pronounced Thales as "tallies" (see footnote).

The theorem
Given triangle ABC and a circle M with AC as the diameter, B lies on the circumference of M if and only if the angle at B is a right angle.
```          B
/ \
/    \
/       \
/          \
/             \
/                \
/                   \
/                      \
A------------------------C
```
The proof
Let the origin of the plane be at the center of M. Then location vector A is the additive inverse of C (i.e. A = -C). The dot product of vector AB and BC is
(A − B) · (B − C) = (A − B) · (B + A) = |A|² − |B
Suppose vectors AB and BC are orthogonal. Since two vectors are orthogonal iff their dot product is 0, it follows |A|² − |B|² = 0, which simplifies to |A| = |B|, so B lies on M. This proves the implication. Clearly the converse also holds.

`Footnote:` Cletus the Foetus /msg'd me and said: Most people pronounce Thales as "thay-leez," but in Greek his name was pronounced "t'-hah-lays," which might explain what your professor was trying to do.

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