page_title: Circle of a sphere
hierarchical_section_title: Circle of a sphere
caption_attribution_description: Português: Uma esfera, um de seus círculos menores, e um triângulo retângulo para determinar o raio do círculo menor.English: A sphere, one of its small circles, and a right triangle to determine the radius of the small circle.
context_page_description: A circle of a sphere is a circle that lies on a sphere. Such a circle can be formed as the intersection of a sphere and a plane, or of two spheres. A circle on a sphere whose plane passes through the center of the sphere is called a great circle; otherwise it is a small circle. Circles of a sphere have radius less than or equal to the sphere radius, with equality when the circle is a great circle.
context_section_description: A circle of a sphere is a circle that lies on a sphere. Such a circle can be formed as the intersection of a sphere and a plane, or of two spheres. A circle on a sphere whose plane passes through the center of the sphere is called a great circle; otherwise it is a small circle. Circles of a sphere have radius less than or equal to the sphere radius, with equality when the circle is a great circle.
caption: B
          
            C
            
              2
            
          
          =
          A
          
            B
            
              2
            
          
          +
          A
          
            C
            
              2
            
          
        
      
      {\displaystyle BC^{2}=AB^{2}+AC^{2}}
    
  , where C is the center of the sphere, A is the center of the small circle, and B is a point in the boundary of the small circle. Therefore, knowing the radius of the sphere, and the distance from the plane of the small circle to C, the radius of the small circle can be determined using the Pythagorean theorem.
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