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If orthocentre and circumcentre of a triangle coincide then is it an equilateral triangle?
Wiki User
∙ 15y ago
Yes. The orthocenter is the intersection of the altitudes; the circumcenter is the intersection of the perpendicular bisectors of the three sides of the triangle. The perpendicular bisector of and altitude to a given side are parallel, so they can coincide at the common center only if they are the same; that means that the opposite vertex is on the perpendicular bisector, so the other two sides are equal. Thus each pair of sides are equal, so the triangle is equilateral.
Wiki User
∙ 15y ago
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What point of concurrency of the perpendicular bisectors of a triangle?
The three perpendicular bisectors (of the sides) of a triangle intersect at the circumcentre - the centre of the circle on which the three vertices of the triangle sit.
What intersects at the circumcenter of a triangle?
The perpendicular bisectors of the sides of a triangle intersect at its circumcentre.
What term describes the point where the three altitudes of a triangle intersect?
It is the orthocentre.
What is a 4cm by 4cm by 4cm triangle called?
It is an equilateral triangle
Is an equilateral triangle be an obtuse triangle?
No, an equilateral triangle can not be an obtuse triangle. All angles in an equilateral triangle are 60o. An obtuse triangle has 1 angle that is greater than 90o.
What triangle has a incenter circumcenter orthocenter and centroid?
Every triangle has an incentre, circumcentre, orthocentre and centroid.
What are the properties of the centroid of a triangle?
Mention all the properties of CENTROID, ORTHOCENTRE, CIRCUMCENTRE ?
What point of concurrency of the perpendicular bisectors of a triangle?
The three perpendicular bisectors (of the sides) of a triangle intersect at the circumcentre - the centre of the circle on which the three vertices of the triangle sit.
What is the answer for triangle abc?
There can be no answer.First, there is no information on the triangle. Second, what is the question about: do you want the lengths of sides, the perimeter, the measures of angles, the area, the lengths of medians, altitudes, the radius of the incentre, orthocentre, circumcentre. Or do you just want to know what colour it is?
What is the Euler line?
In any triangle that is not equilateral, the Euler line is the straight line passing through the orthocentre, circumcentre and centroid. In an equilateral triangle these three points are coincident and so do not define a line.Orthocentre = point of intersection of altitudes.Circumcentre = point of intersection of perpendicular bisector of the sides.Centroid = point of intersection of medians.Euler proved the collinearity of the above three. However, there are several other important points that also lie on these lines. Amongst them,Nine-point Centre = centre of the circle that passes through the bottoms of the altitudes, midpoints of the sides and the points half-way between the orthocentre and the vertices.
What is a measure of center?
The answer depends on the context: a circle has one centre, a triangle has four (centroid, incentre, orthocentre, circumcentre), some shapes have none, statistical (or probability) distributions have two: mean and median (the mode is not necessarily central).
What kind of figure can be rotated less than 360 degrees around the center point and coincide with the original figure?
If it's an *equilateral* triangle, a triangle. Check out quadrilaterals (squares, rectangles), then *equilateral* pentagons, hexagons, etc. Generally, an equilateral polygon needs only rotate (360/number of sides) degrees to coincide.
Where do the altitudes of an acute triangle intersect?
At the orthocentre which is in the interior of the triangle.
What is the intersection of the three altitudes in a triangle?
It is the orthocentre.
Which is the point of intersections of the altitudes in the triangle?
It is the orthocentre.
Which is the point of intersection of the altitudes of a triangle?
It is called the orthocentre.
What intersects at the circumcenter of a triangle?
The perpendicular bisectors of the sides of a triangle intersect at its circumcentre.
