Sagot :
2) b.
x0 = (a²+R²-R'²)/2a
y0² = R² - x0²
y0² = R² - (a²+R²-R'²)²/4a²
= R² - ((a²+R²)² - 2R'²(a²+R²) + R'4)/4a²
= (4a²R² - a4 - 2a²R² - R4 + 2R'²a² + 2R'²R² - R'4)/4a²
= (R'²(2a² + 2R²) + 2a²R² - a4 - R4 - R'4)/4a²
= (R'²((a+R)²+(a-R)²) - (a² - R²)² - R'4)/4a²
= (R'²((a+R)²+(a-R)²) -(a-R)²(a+R)² - R'4)/4a²
= ((a+R)²-R'²)(R'² - (a-R)²)/4a²
= (a+R+R')(a+R-R')(a-R+R')(-a+R+R')/4a²
c.
a+R+R' > 0 et a+R-R' > 0 (car R>R')
0 R-R' R+R'
a-R+R' - 0 + +
-a+R+R' + + 0 -
y0² - + -