page_title: Orthodiagonal quadrilateral
section_title: Infinite sets of inscribed rectangles
hierarchical_section_title: Orthodiagonal quadrilateral / Infinite sets of inscribed rectangles
caption_attribution_description: English: A set of inscribed rectangles defined by Pascal-points circles
context_page_description: In Euclidean geometry, an orthodiagonal quadrilateral is a quadrilateral in which the diagonals cross at right angles. In other words, it is a four-sided figure in which the line segments between non-adjacent vertices are orthogonal to each other.
context_section_description: For every orthodiagonal quadrilateral, we can inscribe two infinite sets of rectangles:
  (i) a set of rectangles whose sides are parallel to the diagonals of the quadrilateral
  (ii) a set of rectangles defined by Pascal-points circles.
caption: A
          B
          C
          D
        
      
      {\displaystyle ABCD}
    
   is an orthodiagonal quadrilateral. 
    
      
        
          
            P
            
              1
            
          
        
      
      {\displaystyle P_{1}}
    
   and 
    
      
        
          
            Q
            
              1
            
          
        
      
      {\displaystyle Q_{1}}
    
   are Pascal points formed by the circle 
    
      
        
          
            ω
            
              1
            
          
        
      
      {\displaystyle \omega _{1}}
    
  , 
    
      
        
          
            σ
            
              
                P
                
                  1
                
              
              
                Q
                
                  1
                
              
            
          
        
      
      {\displaystyle \sigma _{P_{1}Q_{1}}}
    
   is Pascal-points circle which defines the rectangle 
    
      
        
          
            P
            
              1
            
          
          
            V
            
              1
            
          
          
            Q
            
              1
            
          
          
            W
            
              1
            
          
        
      
      {\displaystyle P_{1}V_{1}Q_{1}W_{1}}
    
  . 
    
      
        
          
            P
            
              2
            
          
        
      
      {\displaystyle P_{2}}
    
   and 
    
      
        
          
            Q
            
              2
            
          
        
      
      {\displaystyle Q_{2}}
    
   are Pascal points formed by the circle 
    
      
        
          
            ω
            
              2
            
          
        
      
      {\displaystyle \omega _{2}}
    
  , 
    
      
        
          
            σ
            
              
                P
                
                  2
                
              
              
                Q
                
                  2
                
              
            
          
        
      
      {\displaystyle \sigma _{P_{2}Q_{2}}}
    
   is Pascal-points circle which defines the rectangle 
    
      
        
          
            P
            
              2
            
          
          
            V
            
              2
            
          
          
            Q
            
              2
            
          
          
            W
            
              2
            
          
        
      
      {\displaystyle P_{2}V_{2}Q_{2}W_{2}}
    
  .
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