Angles Inside and Outside Circles
Links and useful resources
- gr10's Geometry >>>START HERE<<<
- AoPS Online Textbook
- AoPS Alcumus
- Big Ideas Geometry textbook
- GeoGebra Online Geometry Constuction Tool
- Two-column math templates
- Proofs unit slides from mathgiraffe.com
- Proofs unit printables for two-column proofs
Lesson-specific resource links
Concept summary and connections
- secant - line that intersects circle in two points
- Draw lines to create actual inscribed angles (the secant lines will have four intersection points)
- Use inscribed angles to figure out the other angles in the triangles that you created.
Any time you have secant lines that form an angle, you'll have four points of intersection to work with on the circle. You can add lines between those points to create inscribed angles, and those will give you a lot of information about the other angles in the diagram because of triangles that are created.
That's particularly helpful if the secant lines intersect inside the circle.
If they intersect outside the circle, the inscribed angles will give you supplementary angles along with triangles. Use them both to compute the angles involved (whether they are angles, or arc angles).
General Formula for secant angle that intersects outside of circle:
The angle of intersection of the secant lines is equal to half of the difference between the arcs they intercept: