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Circles Review

Circles Review. P. Circle -The set of all points in a plane that are equidistant from a given point called the center of the circle. Radius -A segment whose endpoints are the center of the circle and a point in the circle. Diameter -A chord that passes through the center of the circle. .

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Circles Review

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  1. Circles Review

  2. P Circle -The set of all points in a plane that are equidistant from a given point called the center of the circle. Radius -A segment whose endpoints are the center of the circle and a point in the circle. Diameter -A chord that passes through the center of the circle. F P F G P

  3. A G Chord -A segment whose endpoints are on a circle. Secant -A segment that contains a chord of a circle and has exactly one endpoint outside of the circle. (Segment BA is a secant segment of circle P) Tangent -A line in the plane of a circle that intersects the circle at exactly one point. (Line GK is a tangent) P L B P A P G K

  4. A Central Angle -An angle whose vertex is the center of a circle. Inscribed Angle -An angle whose vertex is on a circle and whose sides contain chords of a circle. P L A P L

  5. L Central Angle The measure of the central angleequals the measure of the intercepted arc. <LPA = 125 degrees. Circumference The circumference of a circle can be found with the formula C=pD C=pD C=6p C=18.85 P 125 A 6 in P The circumference of circle P is 18.85 inches

  6. Angles with vertex on the circle A Inscribed angle The measure of an inscribed angle is equal to half of the arc it intercepts. <A= 50(1/2) <A= 25 degrees Tangent/Secant intersection The intersection forms an inscribed angle, therefore it equals one half of the intercepted arc. <D=1/2(50) <D=25 degrees P 50 A D 50 P Z

  7. Angles with Vertex outside of circle The angle formed by the interception of secant/secant , secant/tangent, and tangent/tangent lines equals one half of the difference of the intercepted arcs. -Secant/Secant- x = ½(140-50) x = ½(90) x = 45°

  8. -Secant/Tangent- -Tangent/Tangent- x = ½ (205-155) x = ½ (50) x=25 degrees

  9. Vertex inside Circle The measure of an angle formed inside a circle equals one half of the sum of the intercepted arcs.

  10. Area The area of a circle can be found with the equation A=pr2. A=pr2 A=p9 A=28.27 in2 The area of a sector can be found with the equation A= r2p(x/360) A=152p(60/360) A=225p(1/6) A=37.5p

  11. Arc Length The length of an arc can be determined by multiplying the diameter by the fraction of the circle that the arc is, and multiplying this by pie. P 4 PL= 8p(120/360) PL=8(1/3)p 120 L

  12. Segments of chords, secants, and tangents. 2 Chords The product of the segments of one chord equals the product of the segments of the other chord. 2 Secants The product of the secant segment with its external portion equals the product of the other secant segment with its external portion. 4(x)=(5)(8) 4x=40 X=10 8(x+8)=6(10+6) 8x+64=(16)(6) 8x+64=96 8x=32 X=4 8 x 5 x 4 6 P P 8 10

  13. Tangent/Secant If a tangent and a secant intersect outside of the circle, then the square of the measure of the tangent segment equals the product of the measures of the secant segment and its external portion. 102=5(3x+5) 100=15x+25 75x=15 X=5 10 5 P 3x

  14. Equation of a circle The standard equation of a circle is (x - h)2 + (y - k)2 = r2. What would be the equation of a circle whose center is at (3,4) and has a diameter of 8? (X – 3) 2 + (Y – 4) 2 =16

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