Question 4
Let $H,I,O$ be, respectively, the orthocenter, incenter and circumcenter of a triangle. Prove $2IO\ge IH$. Determine exactly when equality holds.
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; the rubric is editorial. Importer multipliers: correct 1, incorrect 0, blank 0.
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; the rubric is editorial. Importer multipliers: correct 1, incorrect 0, blank 0.