Question

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arrange the following steps to correctly construct a circle inscribed in a triangle using the straightedge-compass method.
move the steps up or down to place them in the correct order.

• identify the intersection of the angle bisectors.
• set the compass width from the incenter to the point where the perpendicular line intersects the triangles side.
• identify the intersection of the perpendicular line and the side of the triangle.
• bisect any two angles.
• draw a triangle.
• draw the inscribed circle.

Explanation:

Step1: Start with drawing the triangle

First, we need a triangle to inscribe a circle in it. So the first step is "Draw a triangle".

Step2: Bisect two angles

To find the incenter (the center of the inscribed circle), we bisect any two angles of the triangle. So next is "Bisect any two angles".

Step3: Find intersection of angle bisectors

The intersection of the angle bisectors is the incenter. So "Identify the intersection of the angle bisectors" comes next.

Step4: Find intersection of perpendicular and side

From the incenter, we draw a perpendicular to one of the sides of the triangle and find its intersection with the side. So "Identify the intersection of the perpendicular line and the side of the triangle".

Step5: Set compass width

We set the compass width from the incenter to the point where the perpendicular intersects the side (this is the radius). So "Set the compass width from the incenter to the point where the perpendicular line intersects the triangle's side".

Step6: Draw the inscribed circle

Finally, using the compass with the set radius, we draw the circle centered at the incenter. So "Draw the inscribed circle".

Answer:

1. Draw a triangle
2. Bisect any two angles
3. Identify the intersection of the angle bisectors
4. Identify the intersection of the perpendicular line and the side of the triangle
5. Set the compass width from the incenter to the point where the perpendicular line intersects the triangle's side
6. Draw the inscribed circle