Angle of intersection of two circles:
The angle of intersection of two circles is defined as the angle between the tangents to the two circles at their point of intersection.
Let x² + y² + 2g₁x + 2f₁y + c₁ = 0,
x² + y² + 2g₂x + 2f₂y + c₂ = 0
Orthogonal Circles:
Two circles are said to be intersect orthogonally, if their angle of intersection is right angle.
cos (∠C₁PC₂) = 0
C₁P² + C₂P² - C₁C₂² = 0
g₁² + f₁² - c₁ + g₂² + f₂² - c₂ = g₁² - 2g₁g₂ + 2f₁f₂ + f₂² + f₁² + g₂²
2 (g₁ g₂ + f₁ f₂) = c₁ + c₂
This is the condition for orthogonality of circles.
Not only mathematicians, but Venn diagrams are also loved by the creative people as well. You can find more free Venn Diagram Templates in the diagram community of Creately Venn Diagram Maker . You can use them freely to easily create Venn diagrams.
ReplyDelete