Explanation: Electric field due to +Q charges of edge A, B and C at center is, . For any point P in the plane of ABC then If the triangle were cut out of some uniformly dense material, such as sturdy cardboard, sheet metal, or plywood, the centroid would be the spot where the triangle would balance on the tip of your finger. It is formed by the intersection of the medians. An acute triangle leans to the right but an equilateral triangle is wide and straight. To these, the equilateral triangle is axially symmetric. Finding the radius, r, of the inscribed circle is equivalent to finding the distance from the centroid to the midpoint of one of the sides. A triangle's centroid is the point that maximizes the product of the directed distances of a point from the triangle's sidelines. 1 answer.

It is also called an equiangular triangle because of the three angles of the triangle measure equal to 60 degrees. But as . This set of six triangles associated to the triangle ABCis a special case of the cevasix configuration (see [5] and [7]) when the chosen point is the centroid G.It has the following peculiar property (see [1]). To this, the equilateral triangle is rotationally symmetric at a rotation of 120°or multiples of this. Since all its sides are equal in length, hence it is easy to find the centroid for it. The geometric centroid (center of mass) of the polygon vertices of a triangle is the point G (sometimes also denoted M) which is also the intersection of the triangle's three triangle medians (Johnson 1929, p. 249; Wells 1991, p. 150). The centroid is the centre point of the object. Heights, bisecting lines, median lines, perpendicular bisectors and symmetry axes coincide. Answer: Yes (at incentre) Question 8. To find the centroid, we need to draw perpendiculars from each vertex of the triangle to the opposite sides. Centroid of Equilateral Triangle. Theorem 1.

A. 10 = 30 cm Height of an Equilateral Triangle By applying the Pythagorean theorem for one half… Finding the radius, R, of the circumscribing circle is equivalent to finding the distance from the centroid of the triangle to one of the vertices. What is the relationship between the areas of ∆GPQ, ∆GQR and ∆GPR? They meet with centroid, circumcircle and incircle center in one point. Here as are equal in magnitude and in opposite direction, so electric field at o is zero. Magnetic induction at centroid of current carrying wire bent in the form of equilateral triangle of side a. If the triangle were cut out of some uniformly dense material, such as sturdy cardboard, sheet metal, or plywood, the centroid would be the spot where the triangle would balance on the tip of your finger. The Euler line - an interesting fact It turns out that the orthocenter, centroid, and circumcenter of any triangle are collinear - that is, they always lie on the same straight line called the Euler line, named after its discoverer. In fact, this theorem generalizes: the remaining intersection points determine another four equilateral triangles. Six vertex–midpoint–centroid triangles of ABC. Figure 1.

The triangle which has all its sides equal in length is called an equilateral triangle. One vertex of the equilateral triangle with centroid at the origin and ... One vertex of the equilateral triangle with centroid at the origin and one side as x + y- 2 = 0 is . If the equation of the base of an equilateral triangle is x + y – 2 and the vertex is (2, … The centroid of the equilateral triangle lies at the center of the triangle.

In an equilateral triangle PQR, G is the centroid. To these, the equilateral triangle is axially symmetric. For more, and an interactive demonstration see Euler line definition. The Equilateral Triangle . ; It is one of the points of concurrency of a triangle. Related questions 0 votes. Are three angle bisectors of a triangle meet at a point ? Heights, bisecting lines, median lines, perpendicular bisectors and symmetry axes coincide. As shown in figure, Resultant of , . The centroid is always in the interior of the triangle. To this, the equilateral triangle is rotationally symmetric at a rotation of 120°or multiples of this.


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