# Proof of the inscribed circle’s center of an equilateral triangle

The inscribed circle’s center of a regular triangle lies at the point of intersection of the medians, heights and perpendicular bisectors of this triangle.

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# The circle inscribed into an equilateral triangle. Property 1

# Proof of the inscribed circle’s center of an equilateral triangle

**Proof of the property**

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The inscribed circle’s center of a regular triangle lies at the point of intersection of the medians, heights and perpendicular bisectors of this triangle.

The inscribed circle’s center of a regular triangle

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According to the property of the regular triangle, in a regular triangle, the angle bisector drawn to any side is its height, median and perpendicular bisector.

The inscribed circle’s center of a triangle lies at the intersection of the angle bisectors.

Therefore, the inscribed circle’s center of a triangle lies at the intersection of the heights and medians.

Proof of the property

Definition of an equilateral triangle

The criterion for a regular triangle

The area of an equilateral triangle. Formulas

The perimeter of an equilateral triangle

The angle bisector of a regular triangle. Properties

The height of a regular triangle. Properties

The median of a regular triangle. Properties

The property of the angles of an equilateral triangle

The exterior angle bisectors of an equilateral triangle

Similarity of regular triangle

The circle circumscribed around a regular triangle. The theorems

Symmetry in an equilateral triangle

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