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Omni-MATH / Triangle ABC has AB=4,BC=3, and a right angle at B. Circles ω₁ and ω₂ of equal radii are drawn such that ω₁ is tangent to AB and AC,ω₂ is tangent to BC and AC, and ω₁ is tangent to…

Problem

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problem

Triangle ABCA B C has AB=4,BC=3A B=4, B C=3, and a right angle at BB. Circles ω1\omega_{1} and ω2\omega_{2} of equal radii are drawn such that ω1\omega_{1} is tangent to ABA B and AC,ω2A C, \omega_{2} is tangent to BCB C and ACA C, and ω1\omega_{1} is tangent to ω2\omega_{2}. Find the radius of ω1\omega_{1}.
Plain-text mathematical notation (without MathML)
Triangle ABC has AB=4,BC=3, and a right angle at B. Circles ω₁ and ω₂ of equal radii are drawn such that ω₁ is tangent to AB and AC,ω₂ is tangent to BC and AC, and ω₁ is tangent to ω₂. Find the radius of ω₁.
Original LaTeX notation
Triangle $A B C$ has $A B=4, B C=3$, and a right angle at $B$. Circles $\omega_{1}$ and $\omega_{2}$ of equal radii are drawn such that $\omega_{1}$ is tangent to $A B$ and $A C, \omega_{2}$ is tangent to $B C$ and $A C$, and $\omega_{1}$ is tangent to $\omega_{2}$. Find the radius of $\omega_{1}$.

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Source and history

task_id
d803e65a-da1c-54f0-aba6-70f64395b144
task_key
test--d803e65a-da1c-54f0-aba6-70f64395b144
task_revision_id
1
config / split
/ test

Official source

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