Central Angles and Arcs
Investigate geometric patterns and proofs that utilize the angles at the center of circles.
This course covers a wide range of theorems in classical Euclidean geometry. You'll start by deriving the Central Angle Theorem and Thales' Theorem, then move on to the Power of a Point Theorem, and conclude with an exploration of different types of triangle centers and their presence on the Euler Line.
Our goal is to help you understand and explore the derivations of these theorems, and to give you many opportunities to practice and strengthen your skills applying them!
Circles form a central part of geometry: get started with your first theorems!
Shapes and angles inscribed and circumscribed.
Warm up with this round of practice problems that explore the Inscribed Angle Theorem.
Study the properties of quadrilaterals inscribed inside of circles.
Intersecting lines inside a circle are a special circumstance worth investigating in detail!
Solve a problem assortment that puts all of your new theorems to use!
What happens when lines just barely touch the outside of a circle?
Practice and strengthen the entire set of tools you've learned so far with this final round of challenges.
Master the inner secrets of triangles.
Start your journey into advanced triangles on the right (aka 90-degree) foot.
Combine what you know about Thales and Pythagoras to approach some fascinating problems.
Explore what happens when you connect up one point and one side.
What happens when the triangles are drawn on a regular grid?
The Euler Line will blow your mind.
Learn about the three most commonly used triangle centers and explore how they relate to each other.
Use perpendicular bisectors to experiment with a fourth type of "center."
Prove a profound result that relates the orthocenter, centroid, and circumcenter.
Use trisectors rather than bisectors to get an astonishing result.