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Omni-MATH / Let △ABC be a scalene triangle. Let h_(a) be the locus of points P such that |PB−PC|=|AB−AC|. Let h_(b) be the locus of points P such that |PC−PA|=|BC−BA|. Let h_(c) be the locus o…

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problem

Let △ABC\triangle A B C be a scalene triangle. Let hah_{a} be the locus of points PP such that |PB−PC|=|AB−AC||P B-P C|=|A B-A C|. Let hbh_{b} be the locus of points PP such that |PC−PA|=|BC−BA||P C-P A|=|B C-B A|. Let hch_{c} be the locus of points PP such that |PA−PB|=|CA−CB||P A-P B|=|C A-C B|. In how many points do all of ha,hbh_{a}, h_{b}, and hch_{c} concur?
Plain-text mathematical notation (without MathML)
Let △ABC be a scalene triangle. Let h_(a) be the locus of points P such that |PB−PC|=|AB−AC|. Let h_(b) be the locus of points P such that |PC−PA|=|BC−BA|. Let h_(c) be the locus of points P such that |PA−PB|=|CA−CB|. In how many points do all of h_(a),h_(b), and h_(c) concur?
Original LaTeX notation
Let $\triangle A B C$ be a scalene triangle. Let $h_{a}$ be the locus of points $P$ such that $|P B-P C|=|A B-A C|$. Let $h_{b}$ be the locus of points $P$ such that $|P C-P A|=|B C-B A|$. Let $h_{c}$ be the locus of points $P$ such that $|P A-P B|=|C A-C B|$. In how many points do all of $h_{a}, h_{b}$, and $h_{c}$ concur?

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Source and history

task_id
7ff4f944-bfce-53d6-a7c5-b9b014372575
task_key
test--7ff4f944-bfce-53d6-a7c5-b9b014372575
task_revision_id
1
config / split
/ test

Official source

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