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MATH / Three noncollinear points and a line ℓ are given in the plane. Suppose no two of the points lie on a line parallel to ℓ (or ℓ itself). There are exactly n lines m perpendicular to …

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problem

Three noncollinear points and a line ℓ\ell are given in the plane. Suppose no two of the points lie on a line parallel to ℓ\ell (or ℓ\ell itself). There are exactly nn lines mm perpendicular to ℓ\ell with the following property: the three circles with centers at the given points and tangent to line mm all concur at some point. Find all possible values of nn. Enter all possible values of n,n, separated by commas.
Plain-text mathematical notation (without MathML)
Three noncollinear points and a line ℓ are given in the plane. Suppose no two of the points lie on a line parallel to ℓ (or ℓ itself). There are exactly n lines m perpendicular to ℓ with the following property: the three circles with centers at the given points and tangent to line m all concur at some point. Find all possible values of n.

Enter all possible values of n, separated by commas.
Original LaTeX notation
Three noncollinear points and a line $\ell$ are given in the plane. Suppose no two of the points lie on a line parallel to $\ell$ (or $\ell$ itself). There are exactly $n$ lines $m$ perpendicular to $\ell$ with the following property: the three circles with centers at the given points and tangent to line $m$ all concur at some point. Find all possible values of $n$.

Enter all possible values of $n,$ separated by commas.

level

Level 5

type

Intermediate Algebra

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Source and history

task_id
63d3f809-5a29-5c4f-8b1b-19fded553a9d
task_key
intermediate~5falgebra--test--63d3f809-5a29-5c4f-8b1b-19fded553a9d
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import