Question

a furniture maker has a triarlar piece of wood shaped like the one in the image. she wants to cut the largest possible circular table top from this piece of wood. how can she draw the largest possible circle on the wood? explain or show the steps she needs to take.

Explanation:

Step1: Find the in - center

The largest possible circle that can be inscribed in a triangle is called the incircle. The center of the incircle (in - center) is the intersection point of the angle bisectors of the triangle. So, use a compass to construct the angle bisectors of each angle of the triangular piece of wood.

Step2: Determine the radius

From the in - center, construct a perpendicular to one of the sides of the triangle. The length of this perpendicular segment is the radius of the incircle.

Step3: Draw the circle

Place the point of the compass at the in - center and set the width of the compass to the length of the radius (the perpendicular segment). Then, draw the circle.

Answer:

First, construct the angle bisectors of the triangle to find the in - center. Then, construct a perpendicular from the in - center to a side to get the radius. Finally, use the in - center as the center and the radius to draw the largest possible circle (the incircle) on the triangular wood.