To **find the circumcenter** of any **triangle**, draw the perpendicular bisectors of the sides and extend them. The point at which the perpendicular intersects each other will be the **circumcenter** of that **triangle**.

- Q. What is the nine point circle used for?
- Q. What prior knowledge do learners need to have to be able to construct a nine-point circle?
- Q. How do you find the Circumcenter of a triangle?
- Q. What is Orthocentre formula?
- Q. Is the Orthocenter always inside the triangle?
- Q. What is the formula for centroid?
- Q. What is centroid of a circle?
- Q. What is Orthocentre?
- Q. Why is it called the Orthocenter?
- Q. What is the difference between Orthocenter and centroid?
- Q. Can a centroid be outside of a shape?
- Q. What are the 4 centers of a triangle?
- Q. Is the Circumcenter equidistant from the vertices?
- Q. What is Circumcenter Theorem?
- Q. Does every triangle have a Circumcenter?
- Q. Why is the Incenter equidistant from the sides of a triangle?
- Q. Is equidistant from the sides of a triangle?
- Q. What is the Incentre of the triangle?
- Q. Which points of concurrency are always inside the triangle?
- Q. What is concurrency in geometry?
- Q. What does concurrency mean?
- Q. What is it called when a circle passes through the three vertices of a triangle?
- Q. What are the 4 points of concurrency?
- Q. How do you find a circumscribed circle?

Feuerbach

## Q. What is the nine point circle used for?

A **nine**–**point circle** bisects a line segment going from the corresponding triangle’s orthocenter to any **point** on its circumcircle.

## Q. What prior knowledge do learners need to have to be able to construct a nine-point circle?

As the preparation for the teaching the circumcircle of triangle, **student needs** to **know** the construction of **Nine**–**Point Circle**. **Nine**–**Point Circle can** be constructed by the special line of triangle, altitude line, which **has** been taught in triangle material of 7th grade.

## Q. How do you find the Circumcenter of a triangle?

**Find** the equations of two line segments forming sides of the **triangle**. **Find** the slopes of the altitudes for those two sides. Use the slopes and the opposite vertices to **find** the equations of the two altitudes. Solve the corresponding x and y values, giving you the coordinates of the **orthocenter**.

## Q. What is Orthocentre formula?

The **orthocenter** is the intersecting point for all the altitudes of the triangle. It lies inside for an acute and outside for an obtuse triangle. … Altitudes are nothing but the perpendicular line ( AD, BE and CF ) from one side of the triangle ( either AB or BC or CA ) to the opposite vertex.

## Q. Is the Orthocenter always inside the triangle?

The **orthocenter** is **always** outside the **triangle** opposite the longest leg, on the same side as the largest angle. The only time all three of these centers fall in the same spot is in the case of an equilateral **triangle**.

## Q. What is the formula for centroid?

Then, we can calculate the **centroid** of the triangle by taking the average of the x coordinates and the y coordinates of all the three vertices. So, the **centroid formula** can be mathematically expressed as G(x, y) = ((x1 + x2 + x3)/3, (y1 + y2 + y3)/3).

## Q. What is centroid of a circle?

A **centroid** is the central point of a figure and is also called the geometric center. It is the point that matches to the center of gravity of a particular shape. It is the point which corresponds to the mean position of all the points in a figure. … For instance, the **centroid of a circle** and a rectangle is at the middle.

## Q. What is Orthocentre?

**Orthocenter** – the point where the three altitudes of a triangle meet (given that the triangle is acute) Circumcenter – the point where three perpendicular bisectors of a triangle meet. Centroid- the point where three medians of a triangle meet.

## Q. Why is it called the Orthocenter?

1 Answer. Ortho means “straight, right”. **Orthocenter**, because it is the intersection of the lines passing through the vertices and forming right-angles with the opposite sides. … This circle passes through the feet of the altitudes, the mid-points of the sides, and the mid-points between the **orthocenter** and the vertices.

## Q. What is the difference between Orthocenter and centroid?

The **centroid** (G) of a triangle is the point of intersection of the three medians of the triangle. … The **centroid** is located 2/3 of the way from the vertex to the midpoint of the opposite side. The **orthocenter** (H) of a triangle is the point of intersection of the three altitudes of the triangle.

## Q. Can a centroid be outside of a shape?

It is possible for the **centroid** of an object to be located **outside** of its geometric boundaries. For example, the **centroid** of the curved section shown is located at some distance below it.

## Q. What are the 4 centers of a triangle?

The **four** ancient **centers** are the **triangle** centroid, incenter, circumcenter, and orthocenter.

## Q. Is the Circumcenter equidistant from the vertices?

Since the radii of the circle are congruent, a **circumcenter** is **equidistant** from **vertices** of the triangle. In a right triangle, the perpendicular bisectors intersect ON the hypotenuse of the triangle.

## Q. What is Circumcenter Theorem?

Any point on the perpendicular bisector of a segment is equidistant from the endpoints of the segment. … Since OA=OB=OC , point O is equidistant from A , B and C . This means that there is a circle having its center at the **circumcenter** and passing through all three vertices of the triangle.

## Q. Does every triangle have a Circumcenter?

Theorem: All **triangles** are cyclic, i.e. **every triangle has** a circumscribed circle or circumcircle. … (Recall that a perpendicular bisector is a line that forms a right angle with one of the **triangle’s** sides and intersects that side at its midpoint.) These bisectors will intersect at a point O.

## Q. Why is the Incenter equidistant from the sides of a triangle?

The angle bisectors of the angles of a **triangle** are concurrent (they intersect in one common point). The point of concurrency of the angle bisectors is called the **incenter** of the **triangle**. … Since radii in a circle are of equal length, the **incenter** is **equidistant from the sides** of the **triangle**.

## Q. Is equidistant from the sides of a triangle?

The incenter (I) of the **triangle** is the point on the interior of the **triangle** that **is equidistant** from all **sides**.

## Q. What is the Incentre of the triangle?

The **incenter** is the point where all of the angle bisectors meet in the **triangle**, like in the video. It is not necessarily the center of the **triangle**. Comment on Ethan’s post “The **incenter** is the point where all of the angle b…”

## Q. Which points of concurrency are always inside the triangle?

The centroid is the **point of concurrency** of the three medians in a **triangle**. It is the center of mass (center of gravity) and therefore is **always** located within the **triangle**.

## Q. What is concurrency in geometry?

A point of **concurrency** is where three or more lines intersect in one place. Incredibly, the three angle bisectors, medians, perpendicular bisectors, and altitudes are **concurrent** in every triangle. … So that point right there where three lines intersect would be our point of **concurrency**.

## Q. What does concurrency mean?

multiple computations are happening

## Q. What is it called when a circle passes through the three vertices of a triangle?

The circumcircle of a **triangle** is the **circle** that **passes through** all **three vertices** of the **triangle**. The construction first establishes the circumcenter and then draws the **circle**. circumcenter of a **triangle** is the point where the perpendicular bisectors of the sides intersect.

## Q. What are the 4 points of concurrency?

**What are the four**common**points of concurrency**? The**four**common**points of concurrency**are centroid, orthocenter, circumcenter, and incenter.- What
**point of concurrency**in a triangle is always located inside the triangle? The centroid and incenter of a triangle always lie inside a triangle. Prev. Next.

## Q. How do you find a circumscribed circle?

**Circumscribe** a **Circle** on a Triangle

**Construct**the perpendicular bisector of one side of triangle.**Construct**the perpendicular bisector of another side.- Where they cross is the center of the
**Circumscribed circle**. - Place compass on the center point, adjust its length to reach any corner of the triangle, and draw your
**Circumscribed circle**!

Learn how to find the orthocenter algebraically given 3 vertices of a triangle in this math video tutorial by Mario's Math Tutoring. We discuss what the ort…

## No Comments