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Which term describes the point where the perpendicular bisectors of the three sides of a triangle intersect?
Circumcenter
What is the point where all three angle bisectors of a triangle intersect?
Its technical name is the incenter; it's also the center of the largest circle that can be inscribed within the triangle. (It is also equidistant from the nearest point along each of the three sides, if that's not obvious.)
Can 2 circle and 3 lines get 17 intersection points?
Yes. Draw three line segments so that they cross at three points forming a triangle (with each side extending beyond the vertices of the triangle). Draw one circle to enclose the triangle without touching it to intersect the extended sides at a further 6 points, making 9 points of intersection so far. Draw the second circle slightly shifted (relative to the first) so that it also encloses the triangle (without touching it) creating a further 6 intersection points with the three lines and 2 with the first circle; an additional 8 intersection points making 17 in all.
Are the medians of a triangle equidistant from each vertex?
Every triangle has three medians, just like it has three altitudes, angle bisectors, and perpendicular bisectors. The medians of a triangle are the segments drawn from the vertices to the midpoints of the opposite sides. The point of intersection of all three medians is called the centroid of the triangle. The centroid of a triangle is twice as far from a given vertex than it is from the midpoint to which the median from that vertex goes. For example, if a median is drawn from vertex A to midpoint M through centroid C, the length of AC is twice the length of CM. The centroid is 2/3 of the way from a given vertex to the opposite midpoint. The centroid is always on the interior of the triangle.
In which triangle do the three altitudes intersect outside of the triangle?
Obtuse Triangle
The intersection of the three angle bisectors of a triangle is called the what?
incenter
What is the common intersection of the angle bisectors of a triangle.?
The common intersection of the angle bisectors of a triangle is called the incenter. It is the center of the inscribed circle of the triangle, and is equidistant from the three sides of the triangle.
The incenter of a triangle is equidistant from the three of the triangle?
sides
What is the intersection of three angle bisectors of a triangle called?
Orthocenter My improvement: The three angle bisectors will intersect at a point called the incenter. At this point it also the center of the largest possible circle within the triangle. Since a circle has a center point, this point within the triangle is called the incenter. The three heights of a triangle will meet at a special point called the orthocenter.
What do you called the intersection point of angle bisector?
The three angle bisectors in a triangle always intersect in one point, and this intersection point always lies in the interior of the triangle. The intersection of the three angle bisectors forms the center of the circle in- scribed in the triangle. (The circle which is tangent to all three sides.) The angle bisectors meet at the incenter which has trilinear coordinates.
What point is not on the Euler line?
The centroid, orthocenter, and circumcenter of a triangle all lie on the Euler line; however, the incenter does not. The incenter, which is the intersection of the angle bisectors, represents the center of the triangle's incircle. Unlike the other three points, the incenter's position is influenced by the triangle's angles and side lengths, leading it to be generally located off the Euler line.
Which term describes the point where the three angle bisectors of a triangle intersect?
incenter
When constructing the circumcenter and circumscribed circle of a triangle you need to find the intersection of all three of which type of line?
the perpendicular bisector
What is the incenter of a triangle?
It is the meeting point or point of concurrency of three angle bisectors of a triangle.
What best describes the incenter of a triangle?
the point where the three angle bisectors of the triangle intersect
Which best describes the orthocenter of a triangle?
A. The point where the three altitudes of the triangle intersect. ~Apex
Is this statement true or falseThe incenter of a triangle is equidistant from all three sides of the triangle?
true
