GEOMETRY 3A CHAPTER 10 POWERPOINT PRESENTATION

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GEOMETRY 3A CHAPTER 10 POWERPOINT PRESENTATION. CIRCLES AND SPHERES. LEARNING TARGETS. AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO: IDENTIFY FORMULAS FOR: CIRCUMFERENCE, DIAMETER, RADIUS SOLVE PROBABILITY PROBLEMS DETERMINE THE AREA OF A CIRCLE

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### GEOMETRY 3ACHAPTER 10 POWERPOINT PRESENTATION

CIRCLES AND SPHERES

LEARNING TARGETS
• AFTER YOU COMPLETE THIS CHAPTER, YOU WILL BE ABLE TO:
• IDENTIFY FORMULAS FOR: CIRCUMFERENCE, DIAMETER, RADIUS
• SOLVE PROBABILITY PROBLEMS
• DETERMINE THE AREA OF A CIRCLE
• DEFINE TRIGONOMETRIC RATIOS AND USE THEM
• DETERMINE VOLUME AND SURFACE AREA OF A SPHERE
CIRCLE - VOCABULARY
• CIRCLE: SET OF POINTS AT THE SAME DISTANCE FROM A GIVEN POINT
• RADIUS: (r) DISTANCE BETWEEN THE CENTER OF A CIRCLE AND ANY POINT ON THE CIRCLE
• CHORD: LINE SEGMENT JOINING TWO POINTS ON A CIRCLE
• DIAMETER: (d) A CHORD THAT PASSES THROUGH THE CENTER OF A CIRCLE
• CIRCUMFERENCE: (c)THE COMPLETE LENGTH AROUND A CIRCLE
• QUADRANT: ONE-FOURTH OF A CIRCLE
THE RATIO PI
• Pi = 22/7 or 3.14
• Its symbol is:
Circumference
• Circumference of a circle:
Estimation of Area of Circle
• Area estimation formula: area of a circle = 3r²
• Approximating the area of a circle:
Area and Probability
• Probability means the chances or likelihood of an event happening.
• Suppose you pick any point inside the circle, what is the probability of picking a point in the top semi-circle? 1 out of 2
• If a circle is split into four quadrants, what is the probability of landing on a quadrant with an even number: 1 out of 2
Area of a Circle
• Area = πr² (use when you know the radius)
• Area = ¼πd² (use when you know the diameter)

SECTOR: THE AREA ENCLOSED WITHIN A CENTRAL ANGLE OF A CIRCLE

CENTRAL ANGLE: AN ANGLE WITH ITS VERTEX AT THE CENTER OF A CIRCLE AND THE CIRCLE’S RADII (PLURAL OF RADIUS) AS ITS SIDE

ARC: A PORTION OF A CIRLCE BOUNDED BY TWO DISTINCT POINTS ON THE CIRCLE

More Circle Vocabulary
• Inscribed Angle: An angle formed by two chords that intersect on the circle.
• Intercepted Arc: The arc of a circle within an inscribed angle.
• Tangent: A line that touches but does not intersect a circle.
• Point of Tangency: The point where the tangent touches the circle
CIRLCE VOCABULARY, CONTINUES…
• Perpendicular Bisector: A set of points equidistant from two given points.
• Equidistant: At an equal distance.
• Locus of Points: A set of points that satisfy a certain condition.
And the Circle Vocabulary Just Keeps Coming!!!!
• Circumcircle: A circle that passes through three vertices of a triangle.
• Circumcenter: Center of a circumcircle and located at the intersection of the perpendicular bisectors of any two sides of a triangle.
• Angle Bisector: Locus of points equidistant from the sides of an angle.
• Incircle: A circle inside a triangle and tangent to each of the triangle’s sides.
What That Looks Like!
• Circumcircle & Circumcenter:
Sine, Cosine, Tangent
• Unit Circle: Circle whose radius is one.
• Sine (sin): for an angle of a right triangle, not the right angle, the ratio of the length of the opposite leg divided by the length of the hypotenuse.
• Cosine (cos): for an angle of a right triangle, not the right angle, the ratio of the length of the adjacent leg divided by the length of the hypotenuse.
• Tangent (tan): for an angle of a right triangle, not the right angle, the ratio of the length of the opposite side divided by the length of the adjacent leg.
Trigonometry
• Trigonometry – The branch of mathematics dealing with the relation between the sides and angles of triangles. For right triangles.
The Sphere
• Sphere: Locus of points in space equidistant from a fixed point.
• Great Circle: Circle on a sphere whose center is the center of the sphere and whose radius equals the radius of the sphere.
• Hemisphere: Half of a sphere.
• Poles: Endpoints of the diameter of a sphere.
• Formulas: SA = 4πr² Volume: 4/3πr³