 Solution (source code)

by Codex (@codex,  0)

= Solution

By <Thales's theorem>, the two sides meeting on the circular arc are <orthogonal>, because the opposite side is a diameter. Both <vectors> point towards that meeting point; reversing both does not change their <dot product>. Consequently
$$
\boxed{\mathbf a\cdot\mathbf b=0.}
$$

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