 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2019/paper-1/9/a/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

a \cdot b = 0.

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