Transcript circles and probability

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Volume problem
The diameter of a sphere is 12ft
What is the volume to the nearest tenth?
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Where do you see arcs and angles together?
Basketball
Soccer
Think of the arc around the net/goal
What shot is easier:
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Circles have arcs
Congruent arcs have congruent central angles
Chords – congruent chords are equidistant from
the center and have congruent central angles
Pg. 774 diameter and chords, will be
perpendicular (perpendicular bisector)
http://www.youtube.com/user/EducatorVids?v=I
8kg3hWXjho&feature=pyv&ad=8603464868&kw
=arcs
Angles with circles
equation of circle
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Measure of the angle is
½ the arc
Pg. 781 got it #1 a and
b
Pg. 782 - 787
Inscribed angle
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Starts from the center
of the circle
Central angle
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equation of circle problems
Pg. 801 – 802 (12, 16, 18, 22, 24, 26, 34, 38,
42, 54)
discuss problems from 12-1, 12-2, & 12-3
problems
Pg. 785 #24
Pg. 787 #40
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What is difference between inscribed and
central angle?
How do you find the equation of a circle
within a coordinate plane?
Homework: have a quarter Tuesday
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circle problem
1) write the standard equation of a circle with
center (2, -8) and r = 9
2) write the standard equation of the circle
with center ( -2, 6) and the circle passes
through point ( - 2, 10)
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do you see parabolas in places, if so where?
What is the probability you see one on a daily
basis
Carowinds
Basketball court
St. Louis
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Finish arcs, angles,
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discuss parabolas
(conic sections),
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Measure of the angle is
½ the arc
Pg. 781 got it #1 a and
b
Pg. 782 – 787
Pg. 785 #24
Pg. 787 #40
Inscribed angle
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Starts from the center
of the circle
Central angle
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Lines of symmetry
Domain
Range
Equation of a parabola,
Focus
Directrix
http://www.mathsisfun.com/geometry/parab
ola.html
Conic section – simply the intersection of a
plane and a cone
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http://www.mathwords.com/p/parabola.htm
The focus of a parabola is a fixed point on
the interior of a parabola used in the formal
definition of the curve.
Locus
◦ A word for a set of points that forms a geometric
figure or graph. For example, a circle can be
defined as the locus of points that are all the same
distance from a given point.
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Directrix of a Parabola
◦ A line perpendicular to the axis of symmetry used
in the definition of a parabola.
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The parabola is the curve formed from all the
points (x, y) that are equidistant from the
directrix and the focus.
A parabola must satisfy the conditions listed
above, and a parabola always has a quadratic
equation.
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The "general" form of a parabola's equation is
the one you're used to, y = ax2 + bx + c —
unless the quadratic is "sideways", in which
case the equation will look something like x
= ay2 + by + c.
The important difference in the two equations
is in which variable is squared: for regular
(vertical) parabolas, the x part is squared; for
sideways (horizontal) parabolas, the y part is
squared.
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The "vertex" form of a parabola with its
vertex at (h, k) is:
regular: y = a(x – h)2 + k
sideways: x = a(y – k)2 + h
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conic sections
Parabolas
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arc circle problems: pg. 784 #6, 10, 12, 14,
16, and 18
parabola problem (today or Wednesday)
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equation of circle problems
Pg. 801 – 802 (12, 16, 18, 22, 24, 26, 34, 38,
42, 54)
discuss problems from 12-1, 12-2, & 12-3
problems
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dart boards deal with concentric circles &
inscribed angles
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Darts
Carnival games
Soccer nets
Basketball nets
Activity: concentric circles on the white
board, what is the probability you get a bull’s
eye
Activity: coin toss – if you flip a coin 20 times,
then what is the ratio of heads to tails
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How are central angles and inscribed angles
different and how are they similar?
angle problem practice
1) pg. 181 #6, 8, 10
2) Pg. 181 #16
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review for tomorrow’s test and BIG review for
common exam
If you find yourself finished with all the
problems, correctly, then complete the
following:
Define: experimental probability, simulation,
sample space, and theoretical probability
AND practice parabola stuff using ipad
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Explain a math concept that we have
discussed and been tested on; assume you
are explaining it to a student who will take
Geometry next year.
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Geometric Proability pg. 668
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Prove circles similar
circle angle problem:
1) Radius is 12, what is half the length of the
chord?
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Tangent lines
A) With inscribed shapes
◦ Thm. 12-3; if 2 tangent lines that share a common
endpoint, then the 2 segments are congruent
◦ Pg. 766
B) Lines & quadrilaterals
a tangent line and a radius create a 90 degree
angle (p. 762 & 763)
a quadrilateral = 360 degrees
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Section 12-3
Circle inscribed in a polygon p. 767 #19
P.769 #32
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Central angles
◦ The central angle of a circle is the angle based at
the circle's center.
◦ In other words, the vertex of the angle must be at
the center of the circle.
◦ A central angle is formed by two radii that start at
the center and intersect the circle itself.
◦ Central Angle = Intercepted Arc
◦ http://www.regentsprep.org/Regents/math/geome
try/GP15/CircleAngles.htm
◦ http://www.icoachmath.com/math_dictionary/Cent
ral_Angle.html
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Do you remember formula?
Angle = ½ arc
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Is there an activity that involves circles, but
also involves probability?
darts
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Chapter 12 tangent lines, Pythagorean thm,
and arcs
you must complete today, due before you
leave
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How is your brain improving because you are
learning math? Give an example