Question

a furniture maker has a angular 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 dr the largest possible circle on the wood? explain or show the steps she needs to take.

Explanation:

Step1: Bisect the angles

Use a compass to bisect each of the three angles of the triangular piece of wood. The angle bisectors will intersect at a single point. This point is the in - center of the triangle.

Step2: Draw perpendicular from in - center to a side

From the in - center (the intersection point of the angle bisectors), draw a perpendicular line to one of the sides of the triangle. The length of this perpendicular segment is the radius of the largest possible circle (the incircle) that can be inscribed in the triangle.

Step3: Draw the circle

Place the point of the compass at the in - center and set the radius to the length of the perpendicular segment found in Step 2. Then, draw the circle.

Answer:

The furniture maker should first bisect the three angles of the triangular wood. The intersection of these angle bisectors is the in - center. Then, draw a perpendicular from the in - center to a side (the length of this perpendicular is the radius). Finally, with the in - center as the center and the perpendicular length as the radius, draw the circle. This circle is the largest possible circular table - top that can be cut from the triangular piece of wood.