Question

fill in the blanks, based on the figure to the right. complete parts a and b.
a. point o is the ______ .
b. og = ______ units.
a. point o is the
blank
figure of triangle kjl with point o inside, perpendicular segments to sides, and lengths: kh=20, oh=6, oj segment with part 3, right angles at g, h, i

Explanation:

Step1: Analyze Point O's Role

In a triangle, the point where angle bisectors, perpendicular bisectors, or altitudes meet has specific names. Here, \( OG \perp KJ \), \( OH \perp KL \), \( OI \perp LJ \), and angle bisectors (marked by arcs) meet at O. So O is the incenter (intersection of angle bisectors, also equidistant from sides).

Step2: Find \( OG \) Length

The incenter is equidistant from all sides. \( OH = 6 \) (perpendicular to \( KL \)), so \( OG \) (perpendicular to \( KJ \)) should equal \( OH \), so \( OG = 6 \).

Step3: Confirm Point O's Name

Since O is the intersection of angle bisectors and equidistant from sides, it's the incenter.

Answer:

a. incenter
b. 6