Circumcenter of a Triangle (Braak)

Autor:Jeanine Braak, Bryan Christian, Tim Brzezinski

Tema:Circunferencia Circunscrita, Geometría

Circumcenter of a Triangle

1. Create the midpoint of each side of the triangle. (Use the Midpoint tool- 2nd menu from left) * First click "midpoint or center" tool, then click point "A" and point "C". Next Point "C" and point "B", Then point "B" and point "A". This should create all the midpoints on the lines. 2. Create a perpendicular line through each midpoint. (Use Perpendicular Bisector tool- 4th menu from left) * First click the "perpendicular bisector" tool *Then click 2 vertex points on the triangle. This will create the perpendicular bisector. * Do this on each line. 3. You should note that all of the perpendicular bisectors intersect at a single point. Label this point G. Point G is the circumcenter of the triangle. ( Use the "point" tool- 2nd menu from left) 4 . Use the circle tool and with G as the center, create a circle. (Use "Circle with center through point" tool- 6th menu from left) * Click the center, point G, and pull the circle out to one of the vertices of the triangle.

Circumcenter

What kinds of lines create the circumcenter of a triangle?

Lengths of Segments AG, BG and CG

If you were to draw segments AG, BG and CG, what do you notice about these segments? 1.) Go back up to the picture and draw these segments by using the segment tool- 3rd menu from left. 2.) Then use the distance tool to find the length of each.- 8th menu from the left

Find the lengths of AG, BG and CG. Are they congruent or not congruent?

Marca todas las que correspondan

A
Congruent
B
Not Congruent

Revisa tu respuesta (3)

What are these lines called ( AG, BG and CG) in a circle?

Find the coordinates of the circumcenter for the following triangle. (Hint: Find the midpoints of the lines, then the perpendicular bisectors and finally the center. Circumscribe the triangle.)

Enter the coordinates of the circumcenter for the triangle.

Changing the Triangle

Click on point L and change the dimensions of the triangle. Answer the questions below:

Acute Triangle

Make the triangle an acute triangle (All angles are less than 90 degrees). The circumcenter is:

Marca todas las que correspondan

A
Inside the triangle
B
Outside the triangle
C
On one of the sides of the triangle

Revisa tu respuesta (3)

Obtuse Triangle

Drag point L to make the image an obtuse triangle (one angle greater than 90 degrees). The circumcenter is:

Marca todas las que correspondan

A
Inside the triangle
B
Outside the triangle
C
On one of the sides of the triangle

Revisa tu respuesta (3)

Right Triangle

Drag point L to make the image a right triangle (One angle 90 degrees). The circumcenter is:

Marca todas las que correspondan

A
Inside the triangle
B
Outside the triangle
C
On one of the sides or the triangle

Revisa tu respuesta (3)

Circumcenter of a Triangle (Braak)