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Omni-MATH / Let P and Q be points on line l with PQ=12. Two circles, ω and Ω, are both tangent to l at P and are externally tangent to each other. A line through Q intersects ω at A and B, wit…

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problem

Let PP and QQ be points on line ll with PQ=12P Q=12. Two circles, ω\omega and Ω\Omega, are both tangent to ll at PP and are externally tangent to each other. A line through QQ intersects ω\omega at AA and BB, with AA closer to QQ than BB, such that AB=10A B=10. Similarly, another line through QQ intersects Ω\Omega at CC and DD, with CC closer to QQ than DD, such that CD=7C D=7. Find the ratio AD/BCA D / B C.
Plain-text mathematical notation (without MathML)
Let P and Q be points on line l with PQ=12. Two circles, ω and Ω, are both tangent to l at P and are externally tangent to each other. A line through Q intersects ω at A and B, with A closer to Q than B, such that AB=10. Similarly, another line through Q intersects Ω at C and D, with C closer to Q than D, such that CD=7. Find the ratio AD/BC.
Original LaTeX notation
Let $P$ and $Q$ be points on line $l$ with $P Q=12$. Two circles, $\omega$ and $\Omega$, are both tangent to $l$ at $P$ and are externally tangent to each other. A line through $Q$ intersects $\omega$ at $A$ and $B$, with $A$ closer to $Q$ than $B$, such that $A B=10$. Similarly, another line through $Q$ intersects $\Omega$ at $C$ and $D$, with $C$ closer to $Q$ than $D$, such that $C D=7$. Find the ratio $A D / B C$.

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task_id
023661c3-c71e-5e38-a72e-4609f5b8a375
task_key
test--023661c3-c71e-5e38-a72e-4609f5b8a375
task_revision_id
1
config / split
/ test

Official source

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