Circles (cloned)

Circles

What shape could be more straightforward than a circle? It’s got a radius, a circumference, an area, and just two associated formulas:

• $C=2\pi r$
• $A=\pi r^2$

“What could be easier than that?” many people ask.

Ah, but that’s only a tiny piece of the story with circles. In this course you’ll find 17 (!) different helpful facts and formulas related to circles, covering ground like:

• central angles
• inscribed angles
• chords
• relationships between arcs subtended by crossing lines
• the Power of a Point theorem

So… do you really know circles well enough to avoid common AMC traps?

One example

• If you have a right triangle inscribed in a circle with radius $5$, what’s the length of the triangle’s hypotenuse?

Other related content

When two chords or two secants cross, they create an angle that is related to the lengths of the arcs they subtend on the circumference.

Also, when two chords cross, the “subchords” created by the crossing point have lengths that are related to each other.

These facts are all covered in the quizzes for this section.

What to do

• If everything above was old news to you, then this section should be no problem. Click “complete” below, and we’ll add all the relevant quizzes to your deck. Then, during your short daily practice, we’ll occasionally quiz you on this knowledge in a way that etch it into your memory for good.
• If some or all of this was new to you, then you should still click “complete” below, and add it to your quizzes, but I recommend against adding anything else for today. Instead, work with these new cards for today, and consider adding more fresh knowledge tomorrow. You might also do a bit of research to refresh (or learn for the first time) the rules given above.

Now continue onto your drills by clicking Quizzes in the menu on your left.