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Omni-MATH / Given a point p and a line segment l, let d(p,l) be the distance between them. Let A,B, and C be points in the plane such that AB=6,BC=8,AC=10. What is the area of the region in th…

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problem

Given a point pp and a line segment ll, let d(p,l)d(p, l) be the distance between them. Let A,BA, B, and CC be points in the plane such that AB=6,BC=8,AC=10A B=6, B C=8, A C=10. What is the area of the region in the (x,y)(x, y)-plane formed by the ordered pairs (x,y)(x, y) such that there exists a point PP inside triangle ABCA B C with d(P,AB)+x=d(P,BC)+y=d(P,AC)d(P, A B)+x=d(P, B C)+y=d(P, A C)?
Plain-text mathematical notation (without MathML)
Given a point p and a line segment l, let d(p,l) be the distance between them. Let A,B, and C be points in the plane such that AB=6,BC=8,AC=10. What is the area of the region in the (x,y)-plane formed by the ordered pairs (x,y) such that there exists a point P inside triangle ABC with d(P,AB)+x=d(P,BC)+y=d(P,AC)?
Original LaTeX notation
Given a point $p$ and a line segment $l$, let $d(p, l)$ be the distance between them. Let $A, B$, and $C$ be points in the plane such that $A B=6, B C=8, A C=10$. What is the area of the region in the $(x, y)$-plane formed by the ordered pairs $(x, y)$ such that there exists a point $P$ inside triangle $A B C$ with $d(P, A B)+x=d(P, B C)+y=d(P, A C)$?

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Source and history

task_id
4847c182-32d7-5bef-b6d7-ea9fa36a7498
task_key
test--4847c182-32d7-5bef-b6d7-ea9fa36a7498
task_revision_id
1
config / split
/ test

Official source

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