Question

marissa starts the construction of the inscribed circle of △ pqr, as shown. table with step 1–4 images of triangle construction which step is next in marissa’s construction?
a construct a median to side rp.
b construct a perpendicular bisector to side rp.
c construct a parallel segment to side rp through point m.
d construct a perpendicular segment to side rp through point m.

Explanation:

To construct the inscribed circle (incircle) of a triangle, we first find the incenter (point \( M \) here, which is the intersection of angle bisectors). The next step is to construct a perpendicular from the incenter to one of the sides (to get the radius, as the inradius is the distance from incenter to a side, and we draw the circle with this radius). So we need to construct a perpendicular segment to side \( RP \) through point \( M \).

• Option A: Median is for centroid, not incircle construction. Eliminate.
• Option B: Perpendicular bisector is for circumcenter, not incenter - related for incircle. Eliminate.
• Option C: Parallel segment is not needed for incircle. Eliminate.
• Option D: Constructing a perpendicular from \( M \) to \( RP \) gives the radius, which is the next step for drawing the incircle.

Answer:

D. Construct a perpendicular segment to side \( RP \) through point \( M \).