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SMO 2019 Open Round 1 Question 22

SMO · SMO 2019 Open Round 1

Question 22

Two points $A$ and $B$ are randomly selected on a line segment $OC$. The probability that the segments $OA$, $AB$ and $BC$ form the sides of a triangle is $p$. Find the value of $\left[\frac1p\right]$.

(Note: If you think the answer of $p$ is $0$, enter your answer as $99999$.)