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Secant and Tangents
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BIANCA MOHINI
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Cards (29)
Formula if given the arc and on the circle
Arc
/
2
Formula if given the arc and in the circle
Arc
+
Arc/2
Formula if given the arc and out of the circle
B Arc
-
S Arc
/
2
Formula if given the angle and intersects inside
ab
=
cd
Formula if given the angle and intersects outside with 3 given
a^2 = b(b+c)
Formula if the angle is given and intersects outside
a(a+b) = c(c+d)
c is
on top
β¨
intersects
outside
Exercises
Find the
center
and
radius
of the circle represented by each equation
Life
Performance
Outcomeβ¨
I am a
courageous
,
resourceful explorer
and
problem solver
, demonstrating my
creativity
and
charisma
Standard Form of the Equation of a Circle
π₯ β β
2 + π¦ β
οΏ½
οΏ½ 2
=
π2
Center: (β, π)
Radius
= π
Given the
center
and
radius
of circles, determine the
center-radius
form
Intended Learning Outcomes in Coordinate Geometry
I can illustrate the
center-radius
form of the equation of a circle
I can determine the
center
and
radius
of a circle given its equation and vice versa
I can solve
problems
involving geometric figures on the
coordinate
plane
Exercises
π₯ β 3 2 + π¦ β 5 2 = 4
π₯
2 +
οΏ½
οΏ½2 = 9
π₯ + 4
2 + π¦ β
7
2 = 81
π₯
2 + π¦
+
2 2 = 5
π₯2 + π¦2 = 3
π₯ β 7 2 + π¦ β 9 2
=
25
π₯ + 2 2 + π¦2
=
16
π₯ β
1
2 2 + π¦ + 6 2 = 2
Given the
center
and
radius
of the following circles, determine the
center-radius
form: 1.
Center
3,
β4
; π = 4
Center
(
5
,1); π = 3
Illustrating the center-radius form of the equation of a circle
Ability to illustrate the center-radius form of the equation of a circle
Exercises
Given the
center
and
radius
of circles, determine the center-radius form:
Center:
-8
,
-3
; Radius:
3
Center: (6, -9); Radius:
1/4
Center:
-7
,
4/5
; Radius:
6
Center:
-2/3
,
-3/8
; Radius:
2/3
Center:
-5
,
-1
; Radius: 3
Center:
10
,
-3
; Radius: 2 3
Center: 3.6, -2.5; Radius: 2 6
Center:
4.5
,
1.9
; Radius:
3
5
Determining the
center
and
radius
of a
circle
β¨
Ability to determine the
center
and
radius
of a
circle
given its
equation
and vice versa
Answer:
Part I
(
2
,
6
,
7
) and
Part II
(
2
,
7
,
9
) of Worksheet 11 β
Center-Radius Form
of the
Equation
of a
Circle
(pages
83β84
)
Solving problems involving geometric figures on the coordinate plane
Ability to solve problems involving geometric figures on the coordinate plane
Exercise 3.9
Given the
center
and
radius
of circles, determine the
center-radius
form
EXERCISESβ¨
Determine the
general equation
of the given
circle
given its
center
and
radius
Exercise 3.8
Determine the
center
and
radius
of circles with equations in
center-radius
form
Illustrating the
center-radius
form of the equation of a circle
Determining the
center
and
radius
of a circle given its equation and vice versa
Center and radius
Center: (3,
-3
), Radius:
4
units
Center: (
-2
,
-1
), Radius:
7
units
Center: (
2
,
1
), Radius:
4
units
Center: (
-1
,
-4
), Radius:
2
units
Center: (
-2
,
-6
), Radius:
5
units
Solving problems
involving geometric figures on the coordinate plane
Equation of a circle given its
center
and
radius
β¨
Center
is given as (
h
,
k
) and
radius
as r
Additional exercises provided for determining the general equation of circles given their
center
and
radius
Rewriting general equations of circles to center-radius form
(x - 2)^2 + (y + 5)^2 =
4^2
(x - 4)^2 + (y + 1)^2 =
7^2
(x + 5)^2 + (y - 7)^2 =
4^2
(x + 1)^2 + (y + 2)^2 =
2^2
(x + 2)^2 + (y + 8)^2 = 5^2
Determining the
center
and
length
of the radius from the
general equation of circles