in abc, the angle bisectors meet at point d. point e is on $overline{ac}$, and $overline{de}$ is…

in abc, the angle bisectors meet at point d. point e is on $overline{ac}$, and $overline{de}$ is perpendicular to $overline{ac}$. point f is the location where the perpendicular bisectors of the sides of the triangle meet. what is the radius of the largest circle that can fit inside abc?\na. ad\nb. bd\nc. de\nd. df\ne. ef

in abc, the angle bisectors meet at point d. point e is on $overline{ac}$, and $overline{de}$ is perpendicular to $overline{ac}$. point f is the location where the perpendicular bisectors of the sides of the triangle meet. what is the radius of the largest circle that can fit inside abc?\na. ad\nb. bd\nc. de\nd. df\ne. ef

Answer

Explanation:

Step1: Recall incircle concept

The largest - circle that can fit inside a triangle is called the incircle. The center of the incircle is the in - center, which is the point of intersection of the angle bisectors of the triangle. Here, point $D$ is the in - center as the angle bisectors meet at point $D$.

Step2: Recall radius property of incircle

The radius of the incircle is the perpendicular distance from the in - center to any side of the triangle. Since $DE$ is perpendicular to side $AC$ and $D$ is the in - center, $DE$ is the radius of the incircle.

Answer:

C. $DE$