Question

d is the incenter of \\( \triangle abc \\). the diagram below shows a nearly completed construction of the inscribed circle of \\( \triangle abc \\). complete the construction.

Explanation:

The incenter \(D\) is the intersection of angle bisectors. To complete the inscribed circle, draw a circle centered at \(D\) with radius equal to the distance from \(D\) to any side of \(\triangle ABC\) (this distance is the inradius, measurable by constructing a perpendicular from \(D\) to a side and using that length as radius).

Answer:

Draw a circle with center \(D\) and radius equal to the perpendicular distance from \(D\) to a side of \(\triangle ABC\) (e.g., perpendicular from \(D\) to \(AB\), \(BC\), or \(AC\)). This circle is the inscribed circle of \(\triangle ABC\).