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Omni-MATH / Consider an isosceles triangle T with base 10 and height 12. Define a sequence ω₁,ω₂,… of circles such that ω₁ is the incircle of T and ω_(i+1) is tangent to ω_(i) and both legs of…

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problem

Consider an isosceles triangle TT with base 10 and height 12. Define a sequence ω1,ω2,…\omega_{1}, \omega_{2}, \ldots of circles such that ω1\omega_{1} is the incircle of TT and ωi+1\omega_{i+1} is tangent to ωi\omega_{i} and both legs of the isosceles triangle for i>1i>1. Find the ratio of the radius of ωi+1\omega_{i+1} to the radius of ωi\omega_{i}.
Plain-text mathematical notation (without MathML)
Consider an isosceles triangle T with base 10 and height 12. Define a sequence ω₁,ω₂,… of circles such that ω₁ is the incircle of T and ω_(i+1) is tangent to ω_(i) and both legs of the isosceles triangle for i>1. Find the ratio of the radius of ω_(i+1) to the radius of ω_(i).
Original LaTeX notation
Consider an isosceles triangle $T$ with base 10 and height 12. Define a sequence $\omega_{1}, \omega_{2}, \ldots$ of circles such that $\omega_{1}$ is the incircle of $T$ and $\omega_{i+1}$ is tangent to $\omega_{i}$ and both legs of the isosceles triangle for $i>1$. Find the ratio of the radius of $\omega_{i+1}$ to the radius of $\omega_{i}$.

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Source and history

task_id
02353cd4-8059-525e-abd6-877bf1ecad61
task_key
test--02353cd4-8059-525e-abd6-877bf1ecad61
task_revision_id
1
config / split
/ test

Official source

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