Question

hide sample answer the point at which the angle bisectors of the triangle meet is the incenter, which is also the center of the inscribed circle of the triangle. so, point d is the incenter. part b create a line through point d, perpendicular to $overline{ab}$. mark the intersection of $overline{ab}$ and the perpendicular line, and label it point e. what does $overline{de}$ represent? explain your reasoning

Explanation:

The in - center of a triangle is the center of the inscribed circle. A line from the in - center perpendicular to a side of the triangle represents the radius of the inscribed circle. This is because the inscribed circle is tangent to the sides of the triangle, and the radius of a circle is perpendicular to the tangent at the point of tangency.

Answer:

$\overline{DE}$ represents the radius of the inscribed circle of the triangle. The in - center (point D) is the center of the inscribed circle, and a line from the center of a circle perpendicular to a tangent (side $\overline{AB}$) is the radius of the circle.