MathDB
2013 HMMT Guts #24: Function in terms of Distance

Source:

March 26, 2013
HMMTfunctiongeometry

Problem Statement

Given a point pp and a line segment ll, let d(p,l)d(p,l) be the distance between them. Let AA, BB, and CC be points in the plane such that AB=6AB=6, BC=8BC=8, AC=10AC=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 ABCABC with d(P,AB)+x=d(P,BC)+y=d(P,AC)?d(P,AB)+x=d(P,BC)+y=d(P,AC)?
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