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Omni-MATH / Acute triangle ABC has circumcenter O. The bisector of ∠ABC and the altitude from C to side AB intersect at X. Suppose that there is a circle passing through B,O,X, and C. If …

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problem

Acute triangle ABCA B C has circumcenter OO. The bisector of ∠ABC\angle A B C and the altitude from CC to side ABA B intersect at XX. Suppose that there is a circle passing through B,O,XB, O, X, and CC. If ∠BAC=n∘\angle B A C=n^{\circ}, where nn is a positive integer, compute the largest possible value of nn.
Plain-text mathematical notation (without MathML)
Acute triangle ABC has circumcenter O. The bisector of ∠ABC and the altitude from C to side AB intersect at X. Suppose that there is a circle passing through B,O,X, and C. If ∠BAC=n^(∘), where n is a positive integer, compute the largest possible value of n.
Original LaTeX notation
Acute triangle $A B C$ has circumcenter $O$. The bisector of $\angle A B C$ and the altitude from $C$ to side $A B$ intersect at $X$. Suppose that there is a circle passing through $B, O, X$, and $C$. If $\angle B A C=n^{\circ}$, where $n$ is a positive integer, compute the largest possible value of $n$.

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Source and history

task_id
f5f5621a-ea21-514e-9f12-94ed3f0be924
task_key
test--f5f5621a-ea21-514e-9f12-94ed3f0be924
task_revision_id
1
config / split
/ test

Official source

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