Bradley Mccarthy
11/22/2024 · Junior High School
Exercice 9. Soient les points \( A(-5,4) ; B(-3,6) ; C(-1 ; 2) \) a Écrire l'équation de \( \left(\Delta_{1}\right) \) la médiatrice de \( [A B] \). b Écrire l'équation de \( \left(\Delta_{2}\right) \) la médiatrice de \( [A C] \). c Déterminer les coordonnées de \( \Omega \) le point d'inter- section de \( \left(\Delta_{1}\right) \) et \( \left(\Delta_{2}\right) \). d Déduire l'équation du cercle circonscrit au triangle ABC.
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**Exercice 9.**
Soient les points \( A(-5,4) \), \( B(-3,6) \) et \( C(-1,2) \).
### a) Équation de la médiatrice \( \Delta_{1} \) de \([AB]\)
\[
y = -x + 1
\]
### b) Équation de la médiatrice \( \Delta_{2} \) de \([AC]\)
\[
y = 2x + 9
\]
### c) Coordonnées de \( \Omega \), intersection de \( \Delta_{1} \) et \( \Delta_{2} \)
\[
\Omega\left( -\dfrac{8}{3},\ \dfrac{11}{3} \right)
\]
### d) Équation du cercle circonscrit au triangle \( ABC \)
\[
\left( x + \dfrac{8}{3} \right)^2 + \left( y - \dfrac{11}{3} \right)^2 = \dfrac{50}{9}
\]
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