X₆₉₄–X₇₆₈

Even (p, q) Circumcircle Points

Even trigonometric (p, q) points on the circumcircle and line at infinity, paired with their isogonal conjugates.

5, 6, 7 3, 4, 5 Kepler Kimberling

X₆₉₄–X₇₆₈ (Even (p, q) Circumcircle Points) — 16 representative centers (from 75 in collection) constructed on acute reference triangle \((a, b, c) = (5, 6, 7)\) with unit baseline AB = \(1\).

X₆₉₄ISOGONAL CONJUGATE OF X₃₈₅

X₆₉₄ is the isogonal conjugate of X₃₈₅.

X₆₉₅ISOGONAL CONJUGATE OF X₃₈₄

X₆₉₅ is the isogonal conjugate of X₃₈₄.

X₆₉₆EVEN (- 4, - 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₆₉₆ lies on the line at infinity. The first trilinear coordinate has the form

X₆₉₇EVEN (- 4, - 3) CIRCUMCIRCLE POINT

1/[\(a^{m-1}(b^{n} + c^{n})\) - \(a^{n-1}(b^{m} + c^{m})\)],

hence the name “(m, n)-circumcircle point”.

X₆₉₈EVEN (- 4, - 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₆₉₈ lies on the line at infinity.

X₆₉₉EVEN (- 4, - 2) CIRCUMCIRCLE POINT

X₆₉₉ = X₃₈₅-cross conjugate of X₂₅₁

X₇₀₀EVEN (- 4, - 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₀₀ lies on the line at infinity.

X₇₀₁EVEN (- 4, - 1) CIRCUMCIRCLE POINT

X₇₀₁ = isogonal conjugate of X₇₀₀

X₇₀₂EVEN (- 4, 0) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₀₂ lies on the line at infinity.

X₇₀₃EVEN (- 4, 0) CIRCUMCIRCLE POINT

X₇₀₃ = isogonal conjugate of X₇₀₂

X₇₀₄EVEN (- 4, 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₀₄ lies on the line at infinity.

X₇₀₅EVEN (- 4, 1) CIRCUMCIRCLE POINT

X₇₀₅ = isogonal conjugate of X₇₀₄

X₇₀₆EVEN (- 4, 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₀₆ lies on the line at infinity.

X₇₀₇EVEN (- 4, 2) CIRCUMCIRCLE POINT

X₇₀₇ = isogonal conjugate of X₇₀₆

X₇₀₈EVEN (- 4, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₀₈ lies on the line at infinity.

X₇₀₉EVEN (- 4, 3) CIRCUMCIRCLE POINT

X₇₀₉ = isogonal conjugate of X₇₀₈

X₇₁₀EVEN (- 4, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₁₀ lies on the line at infinity.

X₇₁₁EVEN (- 4, 4) CIRCUMCIRCLE POINT

X₇₁₁ = isogonal conjugate of X₇₁₀

X₇₁₂EVEN (- 3, - 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₁₂ lies on the line at infinity.

X₇₁₃EVEN (- 3, - 2) CIRCUMCIRCLE POINT

X₇₁₃ = isogonal conjugate of X₇₁₂

X₇₁₄EVEN (- 3, - 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₁₄ lies on the line at infinity.

X₇₁₅EVEN (- 3, - 1) CIRCUMCIRCLE POINT

X₇₁₅ = isogonal conjugate of X₇₁₄

X₇₁₆EVEN (- 3, 0) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₁₆ lies on the line at infinity.

X₇₁₇EVEN (- 3, 0) CIRCUMCIRCLE POINT

X₇₁₇ = isogonal conjugate of X₇₁₆

X₇₁₈EVEN (- 3, 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₁₈ lies on the line at infinity.

X₇₁₉EVEN (- 3, 1) CIRCUMCIRCLE POINT

X₇₁₉ = isogonal conjugate of X₇₁₈

X₇₂₀EVEN (- 3, 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₂₀ lies on the line at infinity.

X₇₂₁EVEN (- 3, 0) CIRCUMCIRCLE POINT

X₇₂₁ = isogonal conjugate of X₇₂₀

X₇₂₂EVEN (- 3, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₂₂ lies on the line at infinity.

X₇₂₃EVEN (- 3, 3) CIRCUMCIRCLE POINT

X₇₂₃ = isogonal conjugate of X₇₂₂

X₇₂₄EVEN (- 3, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₂₄ lies on the line at infinity.

X₇₂₅EVEN (- 3, 4) CIRCUMCIRCLE POINT

X₇₂₅ = isogonal conjugate of X₇₂₄

X₇₂₆EVEN (- 2, -1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₂₆ lies on the line at infinity.

X₇₂₇EVEN (- 2, -1) CIRCUMCIRCLE POINT

X₇₂₇ = X₂₃₈-cross conjugate of X₅₈

X₇₂₈INTERSECTION OF LINES X₈X_9 AND X₅₇X_345

X₇₂₈ = X₃₄₆-Ceva conjugate of X₂₀₀

X₇₂₉EVEN (- 2, 0) CIRCUMCIRCLE POINT

X₇₂₉ = Λ(X₂, X₃₉)

X₇₃₀EVEN (- 2, 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₃₀ lies on the line at infinity.

X₇₃₁EVEN (- 2, 1) CIRCUMCIRCLE POINT

X₇₃₁ = isogonal conjugate of X₇₃₀

X₇₃₂EVEN (- 2, 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₃₂ lies on the line at infinity.

X₇₃₃EVEN (- 2, 2) CIRCUMCIRCLE POINT

X₇₃₃ = trilinear pole of line X₆X₆₈₈

X₇₃₄EVEN (- 2, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₃₄ lies on the line at infinity.

X₇₃₅EVEN (- 2, 3) CIRCUMCIRCLE POINT

X₇₃₅ = isogonal conjugate of X₇₃₄

X₇₃₆EVEN (- 2, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₃₆ lies on the line at infinity.

X₇₃₇EVEN (- 2, 4) CIRCUMCIRCLE POINT

X₇₃₇ = isogonal conjugate of X₇₃₆

X₇₃₈ISOGONAL CONJUGATE OF X₇₂₈

X₇₃₈ is the isogonal conjugate of X₇₂₈.

X₇₃₉EVEN (- 1, 0) CIRCUMCIRCLE POINT

X₇₃₉ = trilinear pole of line X₆X₆₆₇

X₇₄₀EVEN (- 1, 1) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₄₀ lies on the line at infinity.

X₇₄₁EVEN (- 1, 1) CIRCUMCIRCLE POINT

X₇₄₁ = Ψ(X₁₉₀, X₃₇)

X₇₄₂EVEN (- 1, 2) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₄₂ lies on the line at infinity.

X₇₄₃EVEN (- 1, 2) CIRCUMCIRCLE POINT

X₇₄₃ = isogonal conjugate of X₇₄₂

X₇₄₄EVEN (- 1, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₄₄ lies on the line at infinity.

X₇₄₅EVEN (- 1, 3) CIRCUMCIRCLE POINT

X₇₄₅ = isogonal conjugate of X₇₄₄

X₇₄₆EVEN (- 1, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₄₆ lies on the line at infinity.

X₇₄₇EVEN (- 1, 4) CIRCUMCIRCLE POINT

X₇₄₇ = isogonal conjugate of X₇₄₆

X₇₄₈INTERSECTION OF LINES X₂X_31 AND X₉X_38

X₇₄₈ = isogonal conjugate of X₇₄₉

X₇₄₉ISOGONAL CONJUGATE OF X₇₄₈

X₇₄₉ is the isogonal conjugate of X₇₄₈.

X₇₅₀INTERSECTION OF LINES X₁X_88 AND X₂X_31

X₇₅₀ = isogonal conjugate of X₇₅₁

X₇₅₁ISOGONAL CONJUGATE OF X₇₅₀

X₇₅₁ is the isogonal conjugate of X₇₅₀.

X₇₅₂EVEN (0, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₅₂ lies on the line at infinity.

X₇₅₃EVEN (0, 3) CIRCUMCIRCLE POINT

X₇₅₃ = isogonal conjugate of X₇₅₂

X₇₅₄EVEN (0, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₅₄ lies on the line at infinity.

X₇₅₅EVEN (0, 4) CIRCUMCIRCLE POINT

X₇₅₅ = isogonal conjugate of X₇₅₄

X₇₅₆CROSSPOINT OF X₁₀ AND X₃₇

X₇₅₆ is the crosspoint of X₁₀ and X₃₇.

X₇₅₇ISOGONAL CONJUGATE OF X₇₅₆

X₇₅₇ is the isogonal conjugate of X₇₅₆.

X₇₅₈EVEN (1, 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₅₈ lies on the line at infinity.

X₇₅₉EVEN (1, 3) CIRCUMCIRCLE POINT

X₇₅₉ = trilinear pole of line X₆X₆₆₁

X₇₆₀EVEN (1, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₆₀ lies on the line at infinity.

X₇₆₁EVEN (1, 4) CIRCUMCIRCLE POINT

X₇₆₁ = isogonal conjugate of X₇₆₀

X₇₆₂TRILINEAR CUBE OF X₃₇

X₇₆₂ = crosssum of X₅₉₃ and X₇₅₇

X₇₆₃ISOGONAL CONJUGATE OF X₇₆₂

X₇₆₃ is the isogonal conjugate of X₇₆₂.

X₇₆₄TRILINEAR CUBE OF X₅₁₃

X₇₆₄ = crosspoint of X₂₄₄ and X₅₁₃

X₇₆₅CEVAPOINT OF X₁ AND X₁₀₀

X₇₆₅ is the cevapoint of X₁ and X₁₀₀.

X₇₆₆EVEN (3, 4) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₆₆ lies on the line at infinity.

X₇₆₇EVEN (3, 4) CIRCUMCIRCLE POINT

X₇₆₇ = trilinear pole of line X₆X₆₉₃

X₇₆₈ODD (- 4, - 3) INFINITY POINT

As the isogonal conjugate of a point on the circumcircle, X₇₆₈ lies on the line at infinity. The first trilinear coordinate has the form