Khan Academy on a Stick
Circles
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Language and notation of the circle
Formal definition of a circle. Tangent and secant lines. Diameters and radii. major and minor arcs
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Circles: radius, diameter, circumference and Pi
A circle is at the foundation of geometry and how its parts relate to each other is both completely logical and a wonder.
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Length of an arc that subtends a central angle
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Finding central angle measure given arc length
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Area of a sector given a central angle
Circle arcs and sectors
This tutorial will review some of the basic of circles and then think about lengths of arcs and areas of sectors.
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Inscribed and central angles
Showing that an inscribed angle is half of a central angle that subtends the same arc
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Measure of circumscribed angle
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Example with tangent and radius
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Hypotenuse of right triangle inscribed in circle
Central, inscribed and circumscribed angles
We'll now dig a bit deeper in our understanding of circles by looking at central, inscribed and circumscribed angles. This is fun and beautiful as is, but you'll also see that it shows up on a lot of math standardized tests. Why do people like to put geometry like this on standardized tests? Because it shows deductive reasoning skills which are super important in every walk of life!
Equation for a circle using the Pythagorean Theorem
Pythagorean theorem and radii of circles
Radius and center for a circle equation in standard form
Completing the square to write equation in standard form of a circleEquation of a circle
You know that a circle can be viewed as the set of all points that whose distance from the center is equal to the radius. In this tutorial, we use this information and the Pythagorean Theorem to derive the equation of a circle.
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SSS to show a radius is perpendicular to a chord that it bisects
More on the difference between a theorem and axiom. Proving a cool result using SSS
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Perpendicular radius bisects chord
Simple proof using RSH postulate to show that a radius perpendicular to a chord bisects it
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Area of inscribed equilateral triangle (some basic trig used)
Problem that requires us to figure out the area of an equilateral triangle inscribed in a circle (A little trigonometry used)
Area of inscribed triangle
This more advanced (and very optional) tutorial is fun to look at for enrichment. It builds to figuring out the formula for the area of a triangle inscribed in a circle!
How far can you see from a plane window