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All regular shapes are similar. The arc measure is the same as the central angle. The formula to find the arc length of a cricle is 2piR * c/360.

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If there is a triangle where one of the sides is the diameter the third point's angle will be 90 degrees.

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If there is a triangle where one of the sides is the diameter the third point's angle will be 90 degrees.

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Thales Theorem

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a straight line passing from side to side through the center of a body or figure, especially a circle or sphere.

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Unknown Angle Problems with Inscribed Angles in Circle

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Unknown Angle Problems with Inscribed Angles in Circle

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-The Inscribed angle is 1/2 the measure of the central angle.
-The Central Angle is twice the measure of the inscribed angle.
-Inscribed Angle Theorem
-Consequence of Inscribed Angle Theorem

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The formula to find the area of a sector is piR^2 * c/360.

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Chords that are the same distance from the center will be the same size.

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Chords that are the same distance from the center will be the same size.

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if a diameter of a circle bisects a chord, then it must be perpendicular to the chord

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Half of the length of a circle

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All of the vocab and parts of a circle.jpeg

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A chord of a circle is a straight line segment whose endpoints both lie on the circle. A secant line, or just secant, is the infinite line extension of a chord. More generally, a chord is a line segment joining two points on any curve, for instance an ellipse

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In a circle, or congruent circles, congruent chords are equidistant from the center.

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In a circle, or congruent circles, congruent chords are equidistant from the center.

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One important thing you should know in lesson 4 is the vocabulary
Arc
Inscribed Angle
Central Angle
Minor Arc
Major Arc

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In a circle, or congruent circles, congruent chords have congruent arcs

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In a circle, or congruent circles, congruent chords have congruent arcs

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An arc is a portion of the circumference of a circle. In the figure above, the arc is the blue part of the circle. Strictly speaking, an arc could be a portion of some other curved shape, such as an ellipse, but it almost always refers to a circle. To avoid all possible mistake, it is sometimes called a circular arc.

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The part of a circle enclosed by two radii of a circle and their intercepted arc. A pie-shaped part of a circle.

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The circumference of a circle is the distance around the circle. It is the circle's perimeter.

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In a circle, parallel chords intercept congruent arcs.

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A line which touches a circle or ellipse at just one point. Below, the blue line is a tangent to the circle c. Note the radius to the point of tangency is always perpendicular to the tangent

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In the same circle, or congruent circles, congruent central angles have congruent arcs

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Another important thing you should know is that the central angle is 2 times bigger than an inscribed angle

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Arc measure is measured by degrees. Arc length is measured by distance. Don't be confused!

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if two chords are congruent, then the center is equidistant from the two chrods 

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if two chords are congruent, then the center is equidistant from the two chrods 

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In the same circle, or congruent circles, congruent central angles have congruent chords.

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arc length: arclength=2 pi r c/360
c= central angle
Formula for Area of a Sector: A (sector) = pi x r^2 (C/360)
Arc Length: The circular distance around an arc is a piece of the circumference.

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Measure of the Central Angle= 2 x Measure of the Inscribed Angle

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Measure of the Central Angle= 2 x Measure of the Inscribed Angle

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a=2b