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What are properties of the circumcenter of a triangle?
When a circle is drawn around a triangle touching each of its 3 vertices the circumcenter of the triangle is found by drawing 3 perpendicular lines at the midpoint of each of its sides and where these lines intersect within the triangle is its circumcenter.Apex: A. The circumcenter is equidistant from each vertex of the triangle. B. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides. C. The circumcenter of an obtuse triangle is always outside it.
Is the orthocenter of a triangle always inside the triangle?
A Triangle's OrthocenterNo, it can be outside the triangle.
When is the orthocenter inside on or outside of the triangle?
Inside: acute angled triangleOn: right angled triangle Outside: obtuse angled triangle.
Which cannot be located outside of a triangle?
the centroid of a triangle
The orthocenter of a triangle may lie outside the triangle since the altitude may not intersect any side of the triangle?
The orthocenter of a triangle may lie outside the triangle because an altitude does not necessarily intersect the sides of the triangle.
Which points of concurrency may lie outside the triangle?
The orthocentre (where the perpendicular bisectors of the sides meet).
Name all types of triangles for which the point of concurrency is inside the triangle?
The answer depends on what point of concurrency you are referring to. There are four segments you could be talking about in triangles. They intersect in different places in different triangles. Medians--segments from a vertex to the midpoint of the opposite side. In acute, right and obtuse triangles, the point of concurrency of the medians (centroid) is inside the triangle. Altitudes--perpendicular segments from a vertex to a line containing the opposite side. In an acute triangle, the point of concurrency of the altitudes (orthocenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Perpendicular bisectors of sides--segments perpendicular to each side of the triangle that bisect each side. In an acute triangle, the point of concurrency of the perpendicular bisectors (circumcenter) is inside the triangle, in a right triangle it is on the triangle and in an obtuse triangle it is outside the triangle. Angle bisectors--segments from a vertex to the opposite side that bisect the angles at the vertices. In acute, right and obtuse triangles, the point of concurrency of the angle bisectors (incenter) is inside the triangle.
What kind of triangle do the perpendicular bisectors intersect in a point outside the triangle?
a right triange
Is the three perpendicular bisector of a triangle intersect at a point in the exterior of the triangle true or false?
The three ANGLE bisectors of a triangle also bisect the sides, and intersect at a point INSIDE the triangle. The angle bisectors are not necessarily perpendicular to them. The perpendicular bisectors of the sides can intersect in a point either inside or outside the triangle, depending on the shape of the triangle.
What is the name of the point at which all of the triangle's perpendicular bisectors intersect?
Circumcenter, this is the center-point of a circle circumscribed around the triangle. If the triangle is obtuse, then this point is outside the triangle and if the triangle is a right triangle, then the point is the midpoint of the hypotenuse.
Is it true that the point of concurrency of any triangle only happens inside the triangle?
Depends on the point of concurrency of what. The point of concurrency of altitudes will be outside in any obtuse triangle.
When is the point of concurrency outside a triangle?
When you have and obtuse triangle and you are trying to find the Orthocenter
What are properties of the circumcenter of a triangle?
When a circle is drawn around a triangle touching each of its 3 vertices the circumcenter of the triangle is found by drawing 3 perpendicular lines at the midpoint of each of its sides and where these lines intersect within the triangle is its circumcenter.Apex: A. The circumcenter is equidistant from each vertex of the triangle. B. The circumcenter is at the intersection of the perpendicular bisectors of the triangle's sides. C. The circumcenter of an obtuse triangle is always outside it.
How do you find the altitude outside of a triangle?
The altitude of a triangle is the distance from the line containing the base to the vertex. Draw the base and continue on outside of the triangle. Measure perpendicular from that line to the vertex.
Do the altidudes of a triangle always meet in the interior of the triangle?
In a obtuse triangle, the point of concurrency, where multiple lines meet, of the altitudes, called the orthocenter, is outside the triangle. In a right angle, the orthocenter lies on the vertex (corner) of the right angle. In an acute angle, the orthocenter lies inside the triangle.
What are the characteristics of orthocenter?
The orthocenter of a triangle is the point where the altitudes of the triangle intersect. It may lie inside, outside, or on the triangle depending on the type of triangle. In an acute triangle, the orthocenter lies inside the triangle; in a right triangle, it is at the vertex opposite the right angle; and in an obtuse triangle, it is outside the triangle.
Is an altitude ever outside a triangle?
Sure. If one of the base angles is more than 90 degrees, then the altitude (height) is outside the triangle. Yes. This only occurs with an obtuse triangle. Because an altitude is a line drawn from a vertex to the opposite side and is perpendicular with that opposite side, it can only occur if it is outside the triangle. Look at the triangle in related links. If you look at the vertex on the top, the only way to draw the altitude would be to draw outside the triangle.
