Triple

Given a phrase, classify it is english named entity (e.g., persons, organizations, works of art) in Latin script, or not (e.g., literals, dates, URLs, verbose phrases). For disambiguation, the statement where the phrase occurs as object is also given. Please return a JSON object with `phrase` (string, the phrase being analyzed) and `is_ne` (boolean, indicating whether the phrase is a Named Entity).

Phrase: Heron’s formula for the area of a triangle | Statement: [Hero of Alexandria, notableConcept, Heron’s formula for the area of a triangle]

Target entity: Heron’s formula for the area of a triangle
Context triple: [Hero of Alexandria, notableConcept, Heron’s formula for the area of a triangle]

• A. Triangle area
  The Triangle area is a metropolitan region in North Carolina anchored by the cities of Raleigh, Durham, and Chapel Hill, known for its universities, research institutions, and technology industry.
• B. Brahmagupta’s theorem
  Brahmagupta’s theorem is a classical result in Euclidean geometry that characterizes a special property of cyclic quadrilaterals whose diagonals are perpendicular, relating the orthocenter of the triangle formed by three vertices to the fourth vertex.
• C. On Triangles of Every Kind
  "On Triangles of Every Kind" is the English title of Regiomontanus’s influential 15th-century treatise on trigonometry, which systematically developed the theory and applications of triangles in mathematics and astronomy.
• D. Trekantsambandet
  Trekantsambandet is a major Norwegian road and bridge network connecting the towns of Stord, Bømlo, and Sveio in western Norway.
• E. Pythagorean theorem
  The Pythagorean theorem is a fundamental principle of geometry stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
• F. None of above. chosen
• G. Unsure - the case is ambiguous/there is not enough information to decide.

Target entity: Heron’s formula for the area of a triangle
Target entity description: Heron’s formula for the area of a triangle is a classical geometric result that expresses a triangle’s area solely in terms of the lengths of its three sides using the semiperimeter.

• A. Triangle area
  The Triangle area is a metropolitan region in North Carolina anchored by the cities of Raleigh, Durham, and Chapel Hill, known for its universities, research institutions, and technology industry.
• B. Brahmagupta’s theorem
  Brahmagupta’s theorem is a classical result in Euclidean geometry that characterizes a special property of cyclic quadrilaterals whose diagonals are perpendicular, relating the orthocenter of the triangle formed by three vertices to the fourth vertex.
• C. On Triangles of Every Kind
  "On Triangles of Every Kind" is the English title of Regiomontanus’s influential 15th-century treatise on trigonometry, which systematically developed the theory and applications of triangles in mathematics and astronomy.
• D. Trekantsambandet
  Trekantsambandet is a major Norwegian road and bridge network connecting the towns of Stord, Bømlo, and Sveio in western Norway.
• E. Pythagorean theorem
  The Pythagorean theorem is a fundamental principle of geometry stating that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides.
• F. None of above. chosen