Question

Sumi is constructing the inscribed circle for △DEF . She has already used her compass and straightedge to complete the part of the construction shown in the figure.

What could be her next step?


Use the straightedge to draw the line through points E and P.

Place the point of the compass on point P and draw an arc that intersects EF¯¯¯¯¯ and DF¯¯¯¯¯ .

Use the straightedge to draw DP−→− .

Place the point of the compass on point P and draw an arc through points G and H.

Answer 1

the answer is c hope this helps

Answer 2

The next step in the construction is:

Use the straightedge to draw DP−→

Explanation:

The steps for the construction of inscribed circle is:

• Bisect one of the angles

• Bisect another angle

• Where they cross is the center of the inscribed circle, called the incenter

• Construct a perpendicular from the center point to one side of the triangle

• Place compass on the center point, adjust its length to where the perpendicular crosses the triangle, and draw your inscribed circle.

Clearly from the figure we could see that Sumi is trying to construct the angle bisector of ∠D as she has drawn the arcs GH by placing the point of compass at point D.

So now she need to join the Point D to Point P to get the angle bisector of ∠D.

Hence the next step in the construction is:

Use the straightedge to draw DP−→