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Dornmegch10

Chords and Arcs
Radius - middle of a circle to any edges of a circle Chord - sgement that has endpoints line on the circle whatever size. Diameter - chord that does contanes the center of the circle you sketch. Centeral Angle - a angle in the plane of a circle whose vertex is the onley center of the circle. Intercepted Arc - interior of the angle of the angle of the centeral angle. Minor Arc - degree measure that is measured of it's centeral angle, the smallest of the angles even when you add the angles up. Major Arc - 360° - dregree measur of it's minor arc. Semicircle is 180°. Arc Legth - L=length, M=degree measure of an arc. L=M/360°(2πr) Chords and Arcs Theorm - In a circle, or in congruent circles, the congruent chords are congruent. Converse of the Chords and Arcs Theorms - in a circle, or congruent circles, then the chords of congruent arcs are congruent. EX. You have a circle with a chord of 9.84 cm. The radius is 4.92 cm, and the M = 170.30. What is the Arc Legth? Hint use that equation. The answer is 14.624. [|Good website that works] [|Chord Link.]

Tangents to Circles
Seants - circle connected to a line that intercets the circle at two points. Tangents - Linr in the plane of the circle that is interction one point of the circle. Known as Point of Tangenty. Tangent Theorm - If a line is tangent to a circle, the the line is perpenduicular to a radius of the circle drawn to the point of tangency. Radius and Cord Theorem - A radius that is perpendicular to a chord of a circle bisects the chord. Converse of the Tangent Theorem - If a line is perpendicular to a radius of a circle at its endpointon the circle, then the line is tangent to the circle. A Theorem - The perpendicular bisector of a chord passes though the center of the circle. ex. Line AB is 30 feet and the same with line CD. AE is 15 ft, BE is 15 ft., and CE is 10 ft. what is x? This is how you do it. 15+15=30. 10+x = 10x. Then divide by 10. The answer is 3. [|Will help you to understand this section.]

Inscribed Angles and Arcs
Inscribed Angle Theorem - The measure of an angle inscribed in a circle is equal to one-half the measure of the intercepted arc. Right Angle Collary - If an inscribed angle intercepts a semicircle, then the angle is a right angle. Arc-Intercept Corollary - If two (2) inscriibed angles intercept the same arc, then they have the same measure. Insribed Angels - Anythig that is inside the circle that you can find. Inscribe Arcs - Arcs that are connected to two points. ex. ABC is a miner arc and it's 40°. So what's the angle measure of A? It's 20°!!! [|Will help you with some things.] Below is by me.

Angles Formed by Sections and Tangents
Theorem -If a tangent and a secant (or a chord) intersectes on a circle ant the point of tangency, then the measure of the angle formed one-half the measure of it's arc. Theorem - The measure of an angle formed by two sencans or chords that intersect in the interior of a circle is one-half the sum of the measure of the arcs intercpted by the angle and it's vertical angle. Theorem - The measure of an angle formed by two secants that intersect in the exterior of a circle is one-half the difference of the measure of the intercepted arcs. Theorem - The measure of a secant-tangent angle with it's vertex outside the circle is one-half the difference of the measures of the intercepted arc. Theorem - The measure of a tangent-tangent angle with it's vertex outside the circle is one-half the difference of the measures of the intercepted arcs, or the measure of the major arc minus 180°. EX. If you have a arc of 355° and you want to know the difference of 180°, what will it be? 355° -180° = 175°. [|Caclulus link] [|Moveing and Groving!!!] [|Orange tagent]

Segment of Tangents, Secants, and Chords
Secant - has two points on the circle. Chords - inside the circle and has two points. Tangents - one point on the circles. Theorem - If two segments are tangent to a circle from the same exteral point, then the segments are equal length. Theorem - If two secants intersect outside a circle, then the product of the lengths of one secant segment and it's external segment equals the product of the lengths of the other secant segment and it's external segment. (Whole x Outside=Whole x Outside) Theorem - If a secant and a tangent intersect outside the circle, then the product of the legths of the secant segment and it's external segment equals the length of the tangent segment².(Whole x Outside=Tangent²) Theorem - If two chords intersect inside a circle, then the product of the lengths of the segment of one chord equals the product of the lengths of the segments of the other chord. Ex. If AB is 55 ft and CD is 55 Ft. AE is 15, BE is 15, CE is 10, and what is DE? 15(15) =225. 10x 225 / 10 = 22.5

Circle in the Coordinate Plane
Equation #1 - x²+y² = r² Equation #2 - (x-h)² +(y-k)² =r² Center = (h,k) __Example__ Trying to find out about a circle in the mittle of a plane. The equation is x²+y²=r² and you know the r value is 144, what do you do? Get down to r 12. the Center(c) = (0,0). Can you find the x and y value? It's simple, I gave you the radius and you have to move it up and down the x and y with the negitive sign. By me.