orthocenter

Meanings

• noun

  The orthocenter of a triangle is the point where the perpendicular bisectors of the sides of the triangle intersect.

  - "Find the orthocenter of triangle ABC."
  - "The orthocenter of triangle XYZ lies on the circumcircle."

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Variants

List of all variants of orthocenter that leads to same result
orthocenter , orthocenters

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Etymology

origin and the way in which meanings have changed throughout history.

From the Greek words 'orthos' meaning 'straight' and 'kentron' meaning 'point'. The term orthocenter refers to the straight point where the perpendicular bisectors intersect.

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Trivia

Any details, considerations, events or pieces of information regarding the word

1. The orthocenter is also the center of the nine-point circle of a triangle.

2. The orthocenter is the only point inside a triangle that is equidistant from all three sides.

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Related Concepts

informations on related concepts or terms closely associated with the word. Discuss semantic fields or domains that the word belongs to

1. Circumcenter: The circumcenter of a triangle is the center of the circle that passes through all three vertices of the triangle.

2. Incenter: The incenter of a triangle is the point where the inradius touches each side of the triangle.

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Culture

Any cultural, historical, or symbolic significance of the word. Explore how the word has been used in literature, art, music, or other forms of expression.

The orthocenter has significance in geometry and mathematics, particularly in the study of triangles.

How to Memorize "orthocenter"

1. visualize
   

   - Imagine a triangle. Draw the perpendicular bisectors of each side. The point where they intersect is the orthocenter.

2. associate
   

   - Associate the orthocenter with the point where perpendicular lines intersect.

3. mnemonics
   

   - Remember: Ortho means straight, center means point. The orthocenter is the point where the straight lines (perpendicular bisectors) intersect.

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