Τρίτη 18 Οκτωβρίου 2022
Κυριακή 26 Απριλίου 2020
Theorem 5
If ABC a triangle then sin²(A/2) , sin²(B/2), sin²(C/2) are roots of the equation:
16R² x³ - 8R ( 2R-ρ ) x² + ( τ² + ρ² -8Rρ ) x -ρ² =0
Theorem 4
If ABC a triangle ,then 1/sinA, 1/sinB,1/sinC are roots of the equation :
2τρ x³ - ( τ ² + ρ² + 4Rρ ) x² +4Rτ x -4R² = 0
Theorem 3
If ABC a triangle then cosA , cosB , cosC are roots of the equation :
4R² x³ - 4R ( R+ρ ) x² + ( τ²+ρ²-4R²) x+ (2R+ρ)² - τ² = 0
Theorem 2
If ABC a triangle then sinA , sinB, sinC are roots of the equation :
4R² x³ -4Rτ x² + ( τ² + ρ² +4Rρ ) x -2τρ=0
Theorem 1
If ABC a triangle with sides of length a,b,c then a,b,c are roots of the equation :
x³ -2τ x² + ( τ² + ρ² + 4 R ρ ) x -4R ρ = 0
τ : semi-perimeter
ρ : radius of the inscribed circle
R : radius of the circumscribed circle
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