Constructing Inscribed Circles in Triangles

This video tutorial teaches how to construct an inscribed circle within a triangle using angle bisectors. It begins with an introduction to angle bisectors and the concept of triangle centers, including the Euler line. The tutorial then defines an inscribed circle as the largest circle within a triangle, with its center at the intersection of the angle bisectors. The video provides a step-by-step guide to constructing the inscribed circle and finding its radius using a perpendicular line segment from the center to a triangle side.

What is an angle bisector?

• A ray that divides an angle into two congruent parts

• A line that divides a triangle into two equal parts

• A segment that connects the midpoints of two sides of a triangle

• A line that is perpendicular to the base of a triangle

Which of the following is true about triangle centers?

• The centroid is the only center of a triangle

• All triangles have only one center

• The Euler line is where all centers meet

• Triangles have multiple centers

What is an inscribed circle?

• A circle that passes through all the vertices of a triangle

• The largest possible circle inside a triangle with sides tangent to it

• A circle that is outside the triangle

• A circle that is tangent to only one side of the triangle

Where is the center of an inscribed circle located?

• At the centroid of the triangle

• At the intersection of the angle bisectors

• At the orthocenter of the triangle

• At the midpoint of the longest side

What is the first step in constructing an inscribed circle?

• Draw the perpendicular bisectors of the sides

• Find the centroid of the triangle

• Draw a circle around the triangle

• Draw a triangle

How do you find the angle bisectors in the construction process?

• By drawing perpendicular lines from the vertices

• By connecting the midpoints of the sides

• By using intersected points from circles drawn on the triangle

• By drawing lines parallel to the sides

What is the role of the blue points in the construction process?

• They are the vertices of the triangle

• They are used to find the angle bisectors

• They mark the midpoint of the sides

• They indicate the center of the inscribed circle

How is the radius of the inscribed circle determined?

• By measuring the longest side of the triangle

• By drawing a perpendicular line from the center to a side

• By using the circumcenter of the triangle

• By finding the midpoint of the base

What tool is used to draw the inscribed circle?

• A ruler

• A protractor

• A compass

• A set square

What is the final step in constructing an inscribed circle?

• Using the compass to draw the circle with the determined radius

• Connecting the midpoints of the sides

• Drawing the circumcircle

• Finding the orthocenter