Geometry Lesson
Circles: From Central Angles to Secants, Tangents & Sector Area
Shared by A STEM Educator
High SchoolThin-SlicingCCSS.MATH.CONTENT.HSG.C.A.2,CCSS.MATH.CONTENT.HSG.C.A.3,CCSS.MATH.CONTENT.HSG.C.B.550 min
Learning Objective
Students will determine arc measures, central and inscribed angle measures, angles formed by chords/secants/tangents, and sector areas using circle theorems.
Lesson Overview
Students progress from identifying central and inscribed angles through arc measures, then tackle chord, secant, and tangent angle relationships, culminating in sector area. Each task changes exactly one variable to build confident mastery.
Materials
- Vertical whiteboards or chart paper
- Dry-erase markers
- Colored markers for arc highlighting
- Rulers/compasses (optional)
- Random grouping tool
Scaffolded Task Progression
1Task 1
In circle $O$ below, central angle $\angle AOB = 64°$. What is the measure of arc $AB$?
```geometry
{"figureType":"circle","radius":3,"centerLabel":"O","circlePoints":[{"label":"A","angle":90},{"label":"B","angle":26}],"radii":["A","B"],"centralAngle":{"from":"A","to":"B","label":"64°"},"title":"Central Angle & Arc"}
```
2Task 2
In circle $O$, central angle $\angle AOB = 64°$. Inscribed angle $\angle ACB$ intercepts the same arc $AB$, where $C$ is a point on the major arc. What is $\angle ACB$?
```geometry
{"figureType":"circle","radius":3,"centerLabel":"O","circlePoints":[{"label":"A","angle":115},{"label":"B","angle":51},{"label":"C","angle":260}],"chords":[{"from":"A","to":"C"},{"from":"C","to":"B"},{"from":"A","to":"B"}],"centralAngle":{"from":"A","to":"B","label":"64°"},"title":"Inscribed Angle Theorem"}
```
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