Circular Geometry

In circle K with m∠JKL=82∘ and JK=7, find the area of sector JKL. Round to the nearest hundredth

35.06 units²

In circle R with m∠QRS=156∘ and QR=10, find the area of sector QRS. Round to the nearest hundredth.

136.14 units²

In circle K with m∠JKL=74∘ and JK=4, find the area of sector JKL. Round to the nearest hundredth.

10.33 units²

In circle T, TU=9 and m∠UTV=160∘. Find the area of shaded sector. Express your answer as a fraction times π.

36π

In circle M, MN=6 and m∠NMO=70∘. Find the area of shaded sector. Express your answer as a fraction times π.

7π

In circle T, m∠UTV=135∘ and the area of the shaded sector = 6π. Find the length of TU.

TU = ___

TU = 4

In circle D with m∠CDE=82∘ and CD=13 units, find the length of CE⌢. Round to the nearest hundredth.

CE = 18.61

In circle P with m∠NPQ=96∘ and NP=3 units, find the length of NQ⌢​. Round to the nearest hundredth.

NQ = 5.03

In circle F with m∠EFG=46∘ and EF=8 units, find the length of EG⌢. Round to the nearest hundredth.

EG = 6.42

In circle P with m∠NPQ=96∘ and NP=19 units, find the length of NQ⌢​. Round to the nearest hundredth.

NQ = 31.83

In circle W, WX=12 and the length of XY⌢=3π. Find m∠XWY.

m∠XWY=45∘

In circle A, AB=5 and m∠BAC=144∘. Find the length of BC⌢. Express your answer as a fraction times π (in simplest form).

Length of BC⌢=4π

In circle C, CD=7 and m∠DCE=30∘. Find the length of DE⌢. Express your answer as a fraction times π (in simplest form).

Length of DE⌢=(7π/6)​

The points L(5,−9),M(6,−5),N(2,−4), and O(1,−8) form quadrilateral LMNO. FIll in the blanks in the image.

I will prove that Quadrilateral LMNO is a square by demonstrating that all sides are of equal measure AND adjacent sides are perpendicular.

To prove all sides are equal:
LM= √17​,  MN= √17​,  NO= √17​,  OL= √17​

All sides are of equal measure.

To prove adjacent sides are perpendicular:
slope of LM= 4,  slope of MN= −1/4​,  slope of NO= 4,  slope of OL= −1/4

The slope of any pair of adjacent sides are negative reciprocals. That being the case, those sides are perpendicular.

Therefore, as a result of these two things taken together, the quadrilateral is a square.

The points B(1,4),C(−5,5),D(−6,−1), and E(0,−2) form quadrilateral BCDE. FIll in the blanks in the image

I will prove that Quadrilateral BCDE is a square by demonstrating that all sides are of equal measure AND adjacent sides are perpendicular.

To prove all sides are equal:
BC= √37​,  CD= √37​,  DE= √37​,  EB= √37​

All sides are of equal measure.

To prove adjacent sides are perpendicular:
slope of BC= −1/6,  slope of CD= 6,  slope of DE= −1/6​,  slope of EB= 6

The slope of any pair of adjacent sides are negative reciprocals. That being the case, those sides are perpendicular.

Therefore, as a result of these two things taken together, the quadrilateral is a square.

The points D(9,8),E(0,6),F(−7,0), and G(2,2) form quadrilateral DEFG. Fill in the blanks

I will prove that Quadrilateral DEFG is a rhombus by demonstrating that all sides are of equal measure.

DE= √85​,  EF= √85​,  FG= √85​,  GD= √85​

All sides are of equal measure.
Therefore the quadrilateral is a rhombus.

Given V(6,−8),W(8,2),X(−6,5), and Y(x,10). Find x such that VW ∥XY.

x=−5

Given J(9,3),K(3,−6),L(5,4), and M(1,y). Find y such that JK∥LM.

y = -2

Given S(0,6),T(−3,−9),U(2,−9), and V(−3,y). Find y such that ST⊥UV.

y = −8

In circle F, m∠GFH=80∘ and the area of shaded sector = (8/9)​π. Find the length of GH⌢. Express your answer as a fraction times π.

(8/9)​π

In circle T, TU=10 and the area of shaded sector = 40π. Find the length of UWV⌢. Express your answer as a fraction times π.

12π

In circle H, HI=4 and the length of IJ⌢=(8/9)​π. Find the area shaded below. Express your answer as a fraction times π.

(16/9)​π

Find the center and radius of the circle represented by the equation below.

x²+y²+2x+8y−19= 0

Center: (−1,−4)  Radius: 6

Find the center and radius of the circle represented by the equation below.

x²+y²−6x−10y+9=0

Center: (3,5)  Radius: 5

Find the center and radius of the circle represented by the equation below.

x²+y²+16x+4y+43=0

Center: (−8,−2)  Radius: 5

Find the center and radius of the circle represented by the equation below.

x²+y²+18x−16y+120=0

Center: (−9,8)  Radius: 5

Find the center and radius of the circle represented by the equation below.

x²+y²−10x+6y−47=0

Center: (5,−3)  Radius: 9

If mMH⌢=56∘ and mQJ⌢​=164∘, find m∠I.

m∠I=54∘

If mIU⌢=125∘ and mLF⌢=147∘, find m∠LJF.

m∠LJF=136∘

If mGH⌢=43∘ and mRK⌢=63∘, find m∠RDK.

m∠RDK=53∘

If mPD⌢=180∘ and m∠Q=58∘, find mLW⌢.

64 = x

If mKM⌢=128∘ and m∠L=42∘, find mZS⌢.

mZS⌢=44∘

MU is tangent to circle O at point G. GA is the circle's diameter. Find m∠MGA.

m∠MGA=90∘

Given the circle below with secants GHI and KJI, find the length of GH. Round to the nearest tenth if necessary.

x ≈ 35.9

Given the circle below with secant LKJ and tangent IJ, find the length of IJ. Round to the nearest tenth if necessary.

x ≈ 19.2

Given the circle below with secant NML and tangent KL, find the length of NM. Round to the nearest tenth if necessary.

x ≈ 14.8

Given the circle below with secants EFG and IHG. If FG=13,HG=12 and EF is 3 less than IH, find the length of IH. Round to the nearest tenth if necessary.

x = 14

Given the circle below with secants PQR​ and TSR. If QR=25,SR=22 and TS is 8 more than PQ, find the length of TS. Round to the nearest tenth if necessary.

19.7

Given the circle below with secants VWX and ZYX. If YX=23,ZY=25 and WX=22, find the length of VW. Round to the nearest tenth if necessary.

x = 28.2

Given the circle below with tangent WX and secant ZYX. If WX=36 and ZX=50, find the length of YX. Round to the nearest tenth if necessary.

x = 25.9

Given the circle below with chords AB and CD. Find the length of AE. Round to the nearest tenth if necessary.

x ≈ 29.4

Given the circle below with chords NO and PQ​. Find the length of QR​. Round to the nearest tenth if necessary.

x = 46.5

Given the circle below with chords UV and WX. Find the length of UY. Round to the nearest tenth if necessary.

x ≈ 15.9