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.

GeometryCirclesArcsAnglesDiameterMajor ArcMinor ArcSemicircle
2025/4/28

1. Problem Description

We are given a circle with center TT. NLNL and MKMK are diameters of circle TT.
In Part A, we need to identify whether arc LKMLKM 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 360360^{\circ}. A semicircle has a measure of 180180^{\circ}. A minor arc has a measure less than 180180^{\circ}, and a major arc has a measure greater than 180180^{\circ}.
The central angle of arc LKLK is 4848^{\circ}, and the central angle of arc KJKJ is 4444^{\circ}. Since MKMK is a diameter, arc MKMK is a semicircle, and its measure is 180180^{\circ}. Thus, the measure of arc LMLM is 18048=132180^{\circ} - 48^{\circ} = 132^{\circ}, and the measure of arc JMJM is 18044=136180^{\circ} - 44^{\circ} = 136^{\circ}.
The measure of arc LKMLKM is the sum of the measures of arcs LKLK and KMKM. Since KMKM is a semicircle, the measure of arc KMKM is 180180^{\circ}. The measure of arc LKLK is 4848^{\circ}.
Therefore, the measure of arc LKMLKM is 180+48=228180^{\circ} + 48^{\circ} = 228^{\circ}. Since 228>180228^{\circ} > 180^{\circ}, arc LKMLKM is a major arc.

3. Final Answer

For Part A:
Arc LKMLKM is a major arc.
The measure of arc LKMLKM is 228228^{\circ}.

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