10.7.1 Write and Graph Equations of Circles Chapter 10: Circles.
10 Circles
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Transcript of 10 Circles
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O IS THE CENTER OF THE CIRCLE, OBCD IS A RECTANGLE AB=3 BD=5FIND THE RADIUS OF THE CIRCLE
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O IS THE CENTER OF THE CIRCLE
Find AE
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GIVEN: O; ;Chords are equidistant from the center of O PROVE:
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GIVEN: O;
ÐPBM@ÐAMB
PROVE:
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O bisects
BT=8RT=BP=2Find ST and AO
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Given O, BC=5, PQ=30
Find the radius of O
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Given O with radius 12 and AB=12; Find OP
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O has radius 12. How far from the center of the circle is a chord with length 12?
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are tangentsAB=30; BC=20; DC=14 Find AD
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O has radius 10P has radius 7O is tangent to P
is tangent to both Find the length of
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THE WALKAROUND PROBLEM
FN=20; NU=14, FU=12F,U, & N are tangent to each other.Find the radii of all three circles.
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THE COMMON EXTERNAL TANGENT PROBLEM
The radius of E=12. The radius of A=8. EA=40 is tangent to both circles. Find its length
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THE COMMON INTERNAL TANGENT PROBLEM
is tangent to A and H. HA=40
The radius of A is 8The radius of H is 12Find RD
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Two circles with radii 8 and 4 are externally tangent. Find the length of the common tangent segment.
C,U & B are tangent.CU=28CB=22BU=25
Find the radius of C
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is a diametermÐA=30AB=13GD=1Find CD and EA.
Given Semicircle W,
TA=4, ST = 6
Find the diameter of the semicircle.
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O has radius 12,
S has radius 9OS=28Find the length of the external and internal common tangent segments to the two circles.
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is tangent to both s.The radius of A=4The radius of B=9Find SM
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DPQR is equilateral
Its sides are tangent to the sides of the smaller of the two concentric circles. If the radius of the larger circle is 12, find the radius of the smaller circle.
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mÐGKD = 80; mÐR=32; Find the measure of all arcs and angles in the diagram
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BIG CIRCLE is tangent to O at F
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IKMJ is a parallelogram JM = 8 ; JI = 10 Find the diameter of the circle
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is a diameter of the circle
AB = 12
Find the diameter of the circle and the measure of all arcs.Find any other thing you can. Can you determine EF?
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Square ABCD has side length 2. A semicircle with diameter is constructed inside the square., and
the tangent to the semicircle from C intersects side at E. What is the length of ?
D C
E
A B
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Circles A,B and C are externally tangent to each other and internally tangent to circle D. Circles B and C are congruent. Circle A has radius 1 and passes through the center of D. What is the radius of circle B?
A
C
B
D
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is a diameter; AB = 12; ;
Find BC, DC, DB & DE
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DABC is drawn in a circle so is a diameter and ÐCAB=60. B is on the circle. AB = 10. Find the diameter of the circle and the length of
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A regular hexagon is inscribed in a circle. Each side of the hexagon is 6. Find the diameter of the circle and the distance from the center of the circle to one edge of the hexagon.
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A regular octagon is inscribed in a circle. Each side of the octagon is 8. Find the diameter of the circle and the distance from the center of the circle to one edge of the octagon.
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A regular decagon is named . Find each angle
Diagonals and intersect at B
Find
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The endpoints of the diameter of a circle are the x and y intercepts of the line with equation . Find the radius of the circle and decide if the circle passes through the origin.
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is tangent to the circle
; AB=16The radius of the circle is 10
Find CD, BD
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O is the center of both and
; AC=8The length of = the length of
Find the length of
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DABC is equilateral, cm.Find the length of
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mÐPAC=90A is the centerPA=8Find the total perimeter of the figure
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The curved pieces on either end are semicircles. Find the total perimeter.
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PQ=24 is a
diameter of O is tangent
to O at PmÐQPR=30PS=PR=RS=
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Find mÐN and mÐL
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The two circles are concentric with center O. is tangent to the smaller circle. The radii of the two circles are 6 and 12. Determine the length of
C BP
F
ED
O
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The two circles are concentric with center O. is tangent to the smaller circle at P.
Find the length of
Q
C BP
S
T
O
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A & B are externally tangent. is the common internal tangentThe radius of A is 8.The radius of B is 2Find
CE,DF,BD,DA,mÐCFE (draw it in ) mÐADB and CF
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The circles are concentric and are inscribed in squares. AB=16Find the circumference of the smallest circle pictured
A B
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POWERTM=3
MW=4MS=12
Find PMç
è is tangent FT=8 ;KT=6
Find RTè
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BC=8
DC=6AB=4Find ED
KW=KM=6NR=1Find RW
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Determine x,y,z,w,s and m
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Please do these problems in numerical order.
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Prove
David’s Theorem Given: O,P
tangent to Ptangent to O
Prove: bisects ÐAOK
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STATEMENTS REASONS
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Given: are each tangent to two circlesA is tangent to B at DA is tangent to C at FB is tangent to C at EProve:DABC is equilateral
STATEMENTS REASONS