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 language | English |
|---|---|
| Pages (from-to) | 115-120 |
| Journal | Geometriae Dedicata |
| Volume | 45 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 1993 |