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The diagram provided is of a triangle \( \triangle ABC \) with specific perpendicular lines drawn:

1. \( F, G, H \) are points where perpendiculars from vertex \( E \) meet the respective sides (or their extensions) of \( \triangle ABC \) at right angles.
2. The point \( D \) lies on line segments connecting these perpendiculars.

### Point of Concurrency:
The point \( D \) is the **orthocenter** of triangle \( ABC \). The orthocenter is defined as the common point where the **altitudes** of a triangle intersect.

- **Altitudes** are perpendicular lines drawn from the vertices of a triangle to the opposite sides (or their extensions).
- In this diagram:
  - \( EF \perp AB \),
  - \( EG \perp BC \),
  - \( EH \perp AC \).

Thus, the lines intersecting at \( D \) represent the **altitudes** of \( \triangle ABC \), making \( D \) the orthocenter.

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Would you like a further explanation of orthocenters or related properties? Here are 5 related questions:

1. What are the properties of the orthocenter of a triangle?
2. How is the orthocenter related to the circumcircle of a triangle?
3. How do we construct the orthocenter geometrically?
4. What is the relationship between the orthocenter, centroid, and circumcenter?
5. How does the orthocenter change for different types of triangles (acute, right, obtuse)?

### Tip:
In an **acute triangle**, the orthocenter lies inside the triangle, while in a **right triangle**, it lies at the vertex of the right angle. For an **obtuse triangle**, it lies outside the triangle.

Discover the point of concurrency in a triangle, specifically the orthocenter, where all altitudes meet. This solution explains how altitudes drawn perpendicular from a triangle's vertices to the opposite sides intersect at the orthocenter. Suitable for students in Grades 9-12 studying triangle geometry.

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