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What is the property of the point of concurency in perpendicular bisectors of a triangle?
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∙ 13y ago
circumcenter
Wiki User
∙ 13y ago
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Which term describes the point where the perpendicular bisectors of the three sides of a triangle intersect?
Circumcenter
The point of concurrency for perpendicular bisectors of any triangle is the center of a circumscribed circle true or false?
The perpendicular bisector of ANY chord of the circle goes through the center. Each side of a triangle mentioned would be a chord of the circle therefore it is true that the perpendicular bisectors of each side intersect at the center.
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.
Prove that the tangent at a to the circumcircle of triangle abc is parallel to bc where triangle abc is a isosceles triangle?
The circumcircle of a triangle is the circle that passes through the three vertices. Its center is at the circumcenter, which is the point O, at which the perpendicular bisectors of the sides of the triangle are concurrent. Since our triangle ABC is an isosceles triangle, the perpendicular line to the base BC of the triangle passes through the vertex A, so that OA (the part of the bisector perpendicular line to BC) is a radius of the circle O. Since the tangent line at A is perpendicular to the radius OA, and the extension of OA is perpendicular to BC, then the given tangent line must be parallel to BC (because two or more lines are parallel if they are perpendicular to the same line).
What is the point that is equidistant from the sides of a triangle?
The incentre, the point where the bisectors of the angles meet.
Do the perpendicular bisectors of a triangle always sometimes or never intersect on the triangle?
The perpendicular bisectors only intersect on the triangle when it is an isosceles right triangle.
How many perpendicular bisectors does an equilateral triangle have?
Equilateral triangles have 3 perpendicular bisectors
What type of triangle has 3 angle bisectors that are also perpendicular bisectors?
equilateral triangle
The perpendicular bisectors of a triangle all pass through what point?
all three perpendicular bisectors elongate to meet at the incenter of the triangle.
Do 3 perpendicular bisectors of a triangle intersect at a point in the exterior of the triangle?
Since the intersection of the perpendicular bisectors of a triangle is the center of the inscribed circle (we call it the centroid of a triangle), the answer is no.
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 intersection of the perpendicular bisectors of a triangle?
circumcenter
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 point of concurrency of the perpendicular bisectors of a triangle called?
The circumcenter, the incenter is the point of concurrency of the angle bisectors of a triangle.
Which type of triangle will always have 3 angle bisectors that are also perpendicular bisectors?
equalateral
What is point of concurrency of perpendicular bisectors of a triangle?
It is the circumcentre.
The point of concurrency of the perpendicular bisectors of a triangle?
circumcenter
