Question

What step is similar when constructing a circle inscribed in a triangle and a circle circumscribed about a triangle?
A. Construct the angle bisectors of each angle in the triangle.
B. Construct the perpendicular bisectors of each side of the triangle.
C. Place the compass on a vertex and use the bisectors to draw the circle.
D. Place the compass on the intersection of the bisectors to draw the circle.

Answer 1

The steps for the construction of a circle inscribed in a triangle are as follows:

I. Construct the angle bisectors of two of the angles of the triangle. The point of intersection of the two angle bisectors is the center of the inscribed circle.

II. Construct a perpendicular bisector from the center identified in I above to one side of the triangle.

III. Place the compass on the center (the intersection of the angle bisectors) and the other end at the intersection of the perpendicular bisector and the triangle to draw the circle.


The steps for the construction of a circle circumscribed about a triangle are as follows:

I. Construct the perpendicular bisectors of two of the sides of the triangle. The point of intersection of the perpendicular bisectors is the center of the circumscribed circle.

II. Place the compass on the center identified in I above and the other end in any of the vertices of the triangle to dram the circle.

Therefore, the step that is similar when constructing a circle inscribed in a triangle and a circle circumscribed about a triangle is "Construct the perpendicular bisectors of each side of the triangle." (option B)

Answer 2

The step that exists equivalent when constructing a circle inscribed in a triangle and a circle circumscribed about a triangle stands "Construct the perpendicular bisectors of each side of the triangle." (option B)

What are the steps for the construction of a circle inscribed in a triangle?

The steps for the construction of a circle inscribed in a triangle stand as follows:

• Create the angle bisectors of two of the angles of the triangle. The point of intersection of the two angle bisectors stands at the center of the inscribed circle.
• Construct a perpendicular bisector from the center recognized above to one side of the triangle.
• Put the compass in the center (the intersection of the angle bisectors) and the other end at the intersection of the perpendicular bisector and the triangle to illustrate the circle.

Therefore, the step that exists equivalent when constructing a circle inscribed in a triangle and a circle circumscribed about a triangle stands "Construct the perpendicular bisectors of each side of the triangle." (option B).

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