We are given a circle with center $T$. $NL$ and $MK$ are diameters of circle $T$. In Part A, we need to identify whether arc $LKM$ is a major arc, minor arc, or semicircle, and then find its measure. In Part B, the diagram is the same as in Part A but there is no task associated.
2025/4/28
1. Problem Description
We are given a circle with center . and are diameters of circle .
In Part A, we need to identify whether arc is a major arc, minor arc, or semicircle, and then find its measure.
In Part B, the diagram is the same as in Part A but there is no task associated.
2. Solution Steps
For Part A:
The measure of an arc is equal to the measure of its central angle. The measure of a full circle is . A semicircle has a measure of . A minor arc has a measure less than , and a major arc has a measure greater than .
The central angle of arc is , and the central angle of arc is . Since is a diameter, arc is a semicircle, and its measure is . Thus, the measure of arc is , and the measure of arc is .
The measure of arc is the sum of the measures of arcs and . Since is a semicircle, the measure of arc is . The measure of arc is .
Therefore, the measure of arc is . Since , arc is a major arc.
3. Final Answer
For Part A:
Arc is a major arc.
The measure of arc is .