Скачать или смотреть Geometry Points: Incenter and Angle Bisectors of a Triangle

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The incenter of a triangle is the point at which the angle bisectors of the triangle intersect. It is the center of the largest circle that can fit inside the triangle, known as the incircle. The incenter is equidistant from the three sides of the triangle, which means that the distances from the incenter to each side are equal.

To find the incenter, you can use the intersection of the angle bisectors of the triangle. An angle bisector is a line that divides an angle into two equal parts. For each angle of the triangle, there is a corresponding angle bisector. The incenter is the point of intersection of these three angle bisectors.

The incenter has several interesting properties. One property is that it is the center of the inscribed circle, which means that the radius of the incircle is equal to the distance from the incenter to any of the sides of the triangle. This radius can be found by using the formula:

r = A / s,

where r is the radius of the incircle, A is the area of the triangle, and s is the semiperimeter of the triangle (half the sum of the lengths of the triangle's sides).

Another property of the incenter is that it is the point of concurrency for the three angle bisectors. This means that any line segment connecting the incenter to a point on a triangle's side will bisect the corresponding angle of the triangle.

In summary, the incenter of a triangle is the point of intersection of the triangle's angle bisectors. It is equidistant from the three sides of the triangle and is the center of the inscribed circle. The incenter has several important properties related to the angles and sides of the triangle.

These videos are designed to review and reteach high school Geometry content. My videos cover…

Points, Lines, and Planes,
Angles and Angle Relationships,
Triangles,
Quadrilaterals,
Circles,
Similarity and Proportions,
Congruent Figures,
Coordinate Geometry,
Transformations,
Area and Perimeter,
Volume and Surface Area,
Right Triangles and Trigonometry,
Geometric Proofs,
Constructions,
Non-Euclidean Geometries.

I have many informative videos for Pre-Algebra, Algebra 1, Algebra 2, Geometry, Pre-Calculus, and Calculus. Please check it out:    / nickperich  

Nick Perich
Norristown Area High School
Norristown Area School District
Norristown, Pa
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