Geometry Questions

he center and radius of a circle with equation x 3 2 y 6 4 one center 6 3 r 2 center 3 6 r 4 center 3 6 r 4 center 3 6 r 2 ck is the equation of a circle with center 3 5 that passes though the point 4 10 tone x 3 2 y 5 2 74 x 4 y 10 74 x 3 2 y 5 226 x 4 y 10 226

2 The equation x 6x y 6y 9 0 is an equation of a circle in expanded form Complete the square to find the center and radius and then write the equation of the circle in standard form To earn full credit you must show your work a center b radius c Equation

ow wattage radio station can be heard only within a certain distance from the station On the graph ow the circular region represents that part of the city where the station can be heard and the cen e circle represents the location of the station Which equation represents the boundary for the regic ere the station can be heard ep elect one 4 4 O a x 6 2 y 1 32 b x 6 y 1 32 c x 6 2 y 1 16 Od x 6 2 y 1 16 X

Vrite an equation of a circle with diameter AB where A 3 0 and B 7 6 Answer Vo 0 TU a

e the standard equation for a circle er 10 6 r 6 ct one a x 6 y 10 36 b x 10 y 6 6 c x 10 2 y 6 6 d x 10 2 y 6 36 heck ite the standard equation for a circle ter 6 8 that passes through 0 0 lect one a x 6 2 y 8 196 b x 6 2 y 8 14 c x 6 2 y 8 100 Od x 6 2 y 8 10

y x 4 Graph y x 4 Choose the correct graph below G OB OA 2 2 OC 2 2 OE 3 5 OG The graphs do not intersect oo Determine any points of intersection Choose the correct answer below O C OB 5 3 O D 2 2 and 2 2 OF 5 3 and 3 5 D

The equation of a sphere is similar to the equation of a circle The equation of a sphere with center h j k and radius r is x h y j z k r M 2 3 3 is the center of a sphere passing through T 0 4 2 What is the radius of the sphere What is the equation of the sphere The radius of the sphere is Type exact answers using radicals as needed

Write an equation of a circle with diameter AB A 6 6 B 14 14 Choose the correct answer below OA x 10 y 10 6 OC x 10 y 10 32 O E x 10 y 10 32 OG x 14 y 14 6 OB x 10 y 10 14 OD x 6 y 6 14 OF x 10 y 10 32 OH x 10 y 10 32

Sketch the graphs of each equation Find all points of intersection of the pair of graphs x y 8 y x 4 Graph x y 8 Choose the correct graph below OA OB 15 O C G O D

1 point Consider the triangle below not drawn to scale b C C 11 01 ZA 16 14 ZB 33 768429 a Let a 4 b 8 and ZC 130 Find the length of side c and measure of the angles ZA and ZB in degrees Give your answer to at least 3 d places

What values are required for A and B so that 3pi 4 is a solution to the following question Asin x Bcos 2x 1 A R

QUESTION 17 1 POINT The polynomial f x given below f x x 3 7x 2 24x 32 Find the other has 1 as a zero zeros of f x List the zeros separated by a comma

a building The height of the ros by h t 8t 2 80t 25

e line parallel to g x 6x 8 and passing through the point 4 2 Write the form

Glven Two Points Write the equation of the line with the two given points 5 1 3 and 3 5 6 1 4 and 6 1

Select the simplification that accurately explains the following statement oot 4 2 2 1 4

What is the value of sec 0 if the terminal side of angle 0 intersects the unit circle in the first quadrant at x

Given the triangle below find tan 0 Enter the answer as a fraction Provide your answer below 3 4 5 0

9 O Answer Check Find the diameter of OO A line that appears to be tangent is tangent If your answer is not a whole number round to the nearest tenth 12 to the nearest tenth 24

S hat is mST nswer 100 hat is mZQPT swer A

You focus your camera on a circular fountain Your camera is at the vertex of the angle formed by tangents to the fountain You estimate that the angle is 46 What is the measure of the arc of the circular basin of the fountain that will be in the photograph The measure of the arc of the circular basin of the fountain that will be in the photograph is Simplify your answer HETO AME

APQR is inscribed in a circle with m P 70 m Q 80 and m R 30 What are the measures of PQ QR and PR Type integers or decimals

Find the value of the variable B

ngle Measures a C Question 6 12 4 17 Find the value of c using the given chord and secant lengths in the diagram shown to the right Round to the nearest tenth as needed Points 0 of 1 10 13

K What is the value of y y Type an integer or a decimal

Find the value of x X Type an integer or a decimal to

efer to OC for problems 1 3 Segment DE is tangent to OC D C F elect one DE 4 and CE 8 what is the radius E a 8 6 b 4 3 c 4 d 2 10 DE 8 and EF 4 what is the radius

A piece of cardboard is 2 9 times as long as it is wide It is to be made into a box with an open top by cutting 2 inch squares from each corner and folding up the sides Let x represent the width in inches of the original piece of cardboard Answer the following questions CIC K 2 2 2 2 a Represent the length of the original piece of cardboard in terms of x Length 2 9x in Use integers or decimals for any numbers in the pression b Give the restrictions on x What will be the dimensions of the bottom rectangular base of the box

122 Answer Check Input answer as a b c b 50 Variables For the circle the dot represents the center 39 2 Find the value of the variables For the circle the dot represents the center I a Input answer as a b c

10 i I 1 I I T 1 I 1 I I 1 1 i 1 I 1 I I T i I L I I T I I 1 1 I T I I 1 I 1 8 Find an 6 1 I I I I 1 I I I I 1 I I I I 1 I I I I 1 T I I 1 I I I I 1 I 1 4 2 14 p u I 1 12 1 1 18 1 10 1 16 1 1 1 i 1 1 i 1 4 1 1 6 I 1 2 i I 7 10 12 714 equation for the graph above D I 1 1 1 1 T 1 1 1 1 I 1 1 1 I I 1 1 T 1 I I T I I i 1 1 I 1 1 1 1 4 6 I 1 1 I I 1 1 1 I I I 1 1 I I I I 1 I 1 T i I 1 i 1 T I I 1 i 1 T I I 1 I I T 8 10

1 A student inscribes quadrilateral ABCD inside a circle The measures of angles A B and C are given below Find the measure of each angle of quadrilateral ABCD m A 8x 4 m B 5x 4 m C 7x 4 2 A student inscribes an angle inside a semicircle to form a triangle The measures of the angles that are not the vertex of the inscribed angle are x and 2x 9 Find the measures of all three angles of the triangle Explain how you got your answer

84 a Answer Check nput answer as a b c bo a 78 Co 42 Find the value of the variables For the circle the dot represents the center b 87 36 nput answer as a b c

Find the value of x to the nearest tenth X 4 2 10

Find the values of x and y Lines that appear to be tangent are tangent X Do not include the degree symbol in your answer JO 238

the value of x X ver eck 4 9 6 3 X the value of x to the nearest tenth 18

Find each indicated measure for circle O a mZA b mCE c m c d mZD e mZABE a mZA Do not include the degree symbol in your answer A 740

K Which arc does ZC intercept ZC intercepts EFC FCE CDE Question 1 12 3 1 EO F Points 0 of 1 C O D E 7 por

23 m 4 5x m 5 4 x 5 24 m 2 4x 3 m27 5 x 3 25 m 3 1 26 m 1 m25 x 52 II 35 3 5 6 7 8 4 N Exercises 23 30

D Exercises 17 18 18 Given Find AB DC DB bisects LADC m 1 36 m A

1 Similar polygons The quadrilaterals JKLM and PQRS are similar Find the length x of QR 0 Z M 2 8 X 9 8 S R S

16 Given Find M 43 65 MNL NO and Zs as shown x y and z R 26

1 m A 63 and m B 42 2 m B 39 and m C 820 3 mA m C 57 4 m B 42 and m A m C A Exercises 1 6 03 B

In Exercises 13 to 15 j k and AABC 13 Given m3 L 1 50 m 4 72 m 1 m2 and m25 Find m B A 5 6 3 4 Exercises 13 15 2 1 C

In Exercises 9 and 10 classify the triangle not shown by considering the measures of its angles 9 a All angles of ABC measure 60 b In ADEF mLD 40 and m E 50 10 a In AXYZ m X 123 b In ARST m R 45 m S 65 and m T 70

15 Given Find m 1 122 3 m 5 m22 m3 and m24 41 5

8 a In AXYZ XY YZ b In ARST RS 6 ST 7 and RT 1 8

houses at points R and T in front of the plane With angle measures as indicated find m R 12 000 37 65 R 37 On a map three Los Angeles suburbs are located at points N Newport Beach P Pomona and B Burbank With angle measures as indicated deter mine m N and m P 8 The roofline of a house shows the shape of right triangle ABC with m C 90 If the mea of C B 33 X 2x N

15 Does the relation is complementary to for angles have a reflexive property consider one angle A symmetric property consider two angles A transitive property consider three angles

angles 24 and 26 have been bisected Using intuition what appears to be true of 29 formed by the bisectors 10 Make a sketch to represent two planes that are a parallel b perpendicular 11 Suppose that r is parallel to s and m 2 87 Find a mZ3 c m 1 b m 6 d m27 12 In Euclidean geometry how many lines can be drawn through a point P not on a line l that are a parallel to line e b perpendicular to line 1 2 3 X4 9 56 7 8 1 2 3 4 5 6 7 8 t S 9 Find 19 Given Find 20 In the figure BE L BE par each ot with Ex

c transitive property consider coplanar lines m n and g 6 In a plane 1 m and t 1 m By appearance how are e and related