CENTROID CIRCUMCENTER INCENTER ORTHOCENTER PDF

Circumcenter is the center of the circumcircle, which is a circle passing through all three vertices of a triangle. To draw the circumcenter create any two perpendicular bisectors to the sides of the triangle. The point of intersection gives the circumcenter. A bisector can be created using the compass and the straight edge of the ruler.

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Circumcenter is the center of the circumcircle, which is a circle passing through all three vertices of a triangle. To draw the circumcenter create any two perpendicular bisectors to the sides of the triangle. The point of intersection gives the circumcenter.

A bisector can be created using the compass and the straight edge of the ruler. Set the compass to a radius, which is more than half the length of the line segment. Then make two arcs on either side of the segment with an end as the center of the arc. Repeat the process with the other end of the segment. The four arcs create two points of intersection on either side of the segment.

Draw a line joining these two points with the aid of the ruler, and that will give the perpendicular bisector of the segment. To create the circumcircle, draw a circle with the circumcenter as the center and the length between circumcenter and a vertex as the radius of the circle. Incenter: Incenter is the point of intersection of the three angle bisectors.

Incenter is the center of the circle with the circumference intersecting all three sides of the triangle. To draw the incenter of a triangle, create any two internal angle bisectors of the triangle. The point of intersection of the two angle bisectors gives the incenter.

To draw the angle bisector, make two arcs on each of the arms with the same radius. This provides two points one on each arm on the arms of the angle. Then taking each point on the arms as the centers, draw two more arcs.

The point constructed by the intersection of these two arcs gives a third point. A line joining the vertex of the angle and the third point gives the angle bisector. To create the incircle, construct a line segment perpendicular to any side, which is passing through the incenter.

Taking the length between the base of the perpendicular and the incenter as the radius, draw a complete circle. Orthocenter: Orthocenter is the point of intersection of the three heights altitudes of the triangle. To create the orthocenter, draw any two altitudes of a triangle. A line segment perpendicular to a side passing through the opposing vertex is called a height. To draw a perpendicular line passing through a point, first mark two arcs on the line with the point as the center.

Then, create another two arcs with each of the intersection points as the center. Draw a line segment joining the first point and the finally constructed point, and that gives the line perpendicular to the line segment and passing through the first point.

The point of intersection of the two heights gives the orthocenter. Centroid: Centroid is the point of intersection of the three medians of a triangle. Centroid divides each median in ratio, and the center of mass of a uniform, triangular lamina lies at this point.

To determine the centroid, create any two medians of the triangle. For creating a median, mark the midpoint of a side. Then construct a line segment joining the midpoint and the opposing vertex of the triangle. The point of intersection of the medians gives the centroid of a triangle. What are the differences among Circumcenter, Incenter, Orthocenter and Centroid? Related posts:.

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Orthocenter, Centroid, Circumcenter and Incenter of a Triangle

Orthocenter The orthocenter is the point of intersection of the three heights of a triangle. A height is each of the perpendicular lines drawn from one vertex to the opposite side or its extension. Centroid The centroid is the point of intersection of the three medians. A median is each of the straight lines that joins the midpoint of a side with the opposite vertex The centroid divides each median into two segments, the segment joining the centroid to the vertex is twice the length of the length of the line segment joining the midpoint to the opposite side. A perpendicular bisectors of a triangle is each line drawn perpendicularly from its midpoint.

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No other point has this quality. Incenters, like centroids, are always inside their triangles. The above figure shows two triangles with their incenters and inscribed circles, or incircles circles drawn inside the triangles so the circles barely touch the sides of each triangle. The incenters are the centers of the incircles. The circumcenters are the centers of the circumcircles. You can see in the above figure that, unlike centroids and incenters, a circumcenter is sometimes outside the triangle. The circumcenter is Inside all acute triangles On all right triangles at the midpoint of the hypotenuse Finding the orthocenter Check out the following figure to see a couple of orthocenters.

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