Let S be the circle in the xy-plane defined by the equation x² + y² = 4. Let E₁E₂ and F₁F₂ be the chords of S passing through the point P₀(1, 0) and parallel to the x-axis and the y-axis, respectively. Let G₁G₂ be the chord of S passing through P₀ and having slope -1. Let the tangents to S at E₁ and E₂ meet at E₃, the tangents to S at F₁ and F₂ meet at F₃, and the tangents to S at G₁ and G₂ meet at G₃. Then, the points E₃, F₃, and G₃ lie on the curve.

Co-ordinates of E₁ and E₂ are obtained by solving y = 0 and x² + y² = 4 ∴ E₁(-√3, 0) and E₂(√3, 0)
Co-ordinates of F₁ and F₂ are obtained by solving x = 1 and x² + y² = 4 ∴ F₁(1, √3) and F₂(1, -√3)
Tangent at E₁: -√3x + y = 4
Tangent at E₂: √3x + y = 4
∴ E₃(0, 4)
Tangent at F₁: x + √3y = 4
Tangent at F₂: x - √3y = 4
∴ F₃(4, 0)
The equation of the chord G₁G₂ is y - 0 = -1(x - 1) ∴ y = -x + 1
Solving this with x² + y² = 4, we get
x² + (-x + 1)² = 4
2x² - 2x - 3 = 0
x = (2 ± √16)/4 = (1 ± √5)
Then y = -x + 1 = (-1 ± √5)
G₁((1 + √5)/2, (-1 + √5)/2), G₂((1 - √5)/2, (-1 - √5)/2)
The equation of the tangents are
(1 + √5)/2 x + (-1 + √5)/2 y = 4
(1 - √5)/2 x + (-1 - √5)/2 y = 4
Solving these two equations, we get G₃(2, 2)
(0, 4), (4, 0) and (2, 2) lies on x + y = 4