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Omni-MATH / In right triangle ABC, a point D is on hypotenuse AC such that BD⊥AC. Let ω be a circle with center O, passing through C and D and tangent to line AB at a point other than B. Point…

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problem

In right triangle ABCA B C, a point DD is on hypotenuse ACA C such that BD⊥ACB D \perp A C. Let ω\omega be a circle with center OO, passing through CC and DD and tangent to line ABA B at a point other than BB. Point XX is chosen on BCB C such that AX⊥BOA X \perp B O. If AB=2A B=2 and BC=5B C=5, then BXB X can be expressed as ab\frac{a}{b} for relatively prime positive integers aa and bb. Compute 100a+b100 a+b.
Plain-text mathematical notation (without MathML)
In right triangle ABC, a point D is on hypotenuse AC such that BD⊥AC. Let ω be a circle with center O, passing through C and D and tangent to line AB at a point other than B. Point X is chosen on BC such that AX⊥BO. If AB=2 and BC=5, then BX can be expressed as (a)/(b) for relatively prime positive integers a and b. Compute 100a+b.
Original LaTeX notation
In right triangle $A B C$, a point $D$ is on hypotenuse $A C$ such that $B D \perp A C$. Let $\omega$ be a circle with center $O$, passing through $C$ and $D$ and tangent to line $A B$ at a point other than $B$. Point $X$ is chosen on $B C$ such that $A X \perp B O$. If $A B=2$ and $B C=5$, then $B X$ can be expressed as $\frac{a}{b}$ for relatively prime positive integers $a$ and $b$. Compute $100 a+b$.

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task_id
bca7f39a-4906-554b-b550-2c7bd0e912f3
task_key
test--bca7f39a-4906-554b-b550-2c7bd0e912f3
task_revision_id
1
config / split
/ test

Official source

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