Question 151
A circle of radius $r$ is inscribed in a circular sector of radius $R$. The length of the $AB$ string is equal to $2a$. Prove that $$
\frac{1}{r} = \frac{1}{R} + \frac{1}{a}
$$
\frac{1}{r} = \frac{1}{R} + \frac{1}{a}
$$
MathNet 2026 — Part 02 Question 151
Math Olympiad Vault · MathNet 2026 — Part 02