Triangle in a triangle : on a problem of Steinhaus

K.A. Post

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8 Citations (Scopus)
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Abstract

A necessary and sufficient condition on the sidesp, q, r of a trianglePQR and the sidesa, b, c of a triangleABC in order thatABC contains a congruent copy ofPQR is the following: At least one of the 18 inequalities obtained by cyclic permutation of {a, b, c} and arbitrary permutation of {itp, q, r} in the formula Max{F(q²+r²-p²), F'(b²+c²-a²)} + Max{F(p²+r²-q²),F'(a²+c²-b²)} = 2Fcr satisfied. In this formula F and F: F=¼(2a²b² + 2b²c² + 2c²a² - a4 - b4 - c4) ¹'² F=¼(2p²q² + 2q²r² + 2r²p² - p4 - q4 - r4) ¹'²
Original languageEnglish
Pages (from-to)115-120
JournalGeometriae Dedicata
Volume45
Issue number1
DOIs
Publication statusPublished - 1993

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