Here are the solutions to the problems: 1. a) A lies in the interior of the circle because PA < PQ. b) B lies in the exterior of the circle because PB > PQ. c) The circles with radii PQ and PB are called concentric circles. 2. One tangent. 3. 12 4. 15 5. 16

1. 1. Identify the facts about π (Pi)
2. What is the circumference of a circle whose diameter measures 12cm? 24 cm? 16
cm? 33cm?
3. A circle has a circumference of 80π m. What is the measure of the radius of the
given circle?
4. What is the area of a circle whose diameter measures 18cm?
5. A circle has an area of 625π m2. What is the measure of the diameter of the
given circle?
For numbers 6-8, refer to the figure below:
2
6. If the measure of arc AB is 24o and arc CD is 56 degrees, what is the measure of
∠2 ?
7. If m∠1 = 88 and arc CD measures 70o what is the measure of arc AB and the sum
of the measures of arcs AD and BC respectively?
8. If arc CD measures 7b – 12, arc AB measures, 20b – 8, m∠1 = 5b + 4 , what is the
measure of angle 1 and 2?
True or false:
1) The measure of an inscribed angle is half the measure of its intercepted arc.
2) If an inscribed angle intercepts a semi-circle, then the inscribed angle is right.
3) If two inscribed angles intercept the same or congruent arcs, they are also congruent.
4) If a quadrilateral is inscribed in a circle, then the consecutive angles are
supplementary.
5) The measure of a minor arc is half the measure of its central angle.
6) The measure of a minor arc is equal to the measure of its central angle.
7) The measure of a minor arc is twice the measure of its central angle.
8) The measure of a minor arc is 360 minus the measure of its central angle.

2. Given Circle O with DB as the diameter, arc AD measures 80° and m∠E = 30 . Find the
measures of angles 1-6.
Describe the following figures:
1.
2.
3.
F
I
A B G
J
E
4.
Use the given figure to solve for the missing measurements:

3. 1. OR = 12, OP = 13, RP=?
2. OQ = 6, PS = 16, OP=?
3. OR = 12, m∠ROP = 60
OP=?
4. m∠RPS = 150 ,
m∠RPO = ?
5. What kind of triangle is ∆PSR ?
6. OR = 24, OP = 25, RP=?
7. OQ = 5, PS = 15, OP=?
8. OR = 17, m∠ROP = 60
OP=?
9. m∠RPS = 125 ,
m∠RPO = ?
10. What kind of triangle is ∆PRO ?
Use the given figure and the given facts below to find FJ and GH.
In the figure below, VK = VM. If AK = 6x + 3 and EG = 14x + 3 what is GM?

4. Define the following parts of a circle:
1) Chord
2) Diameter
3) Radius
4) Tangent
5) Point of tangency
6) Secant
7) Arc
8) Major arc
9) Minor arc
10)Intercepted Arc
11)Inscribed angle
12)Central Angle
Identify the formula of area and perimeter of a:
1. Triangle
2. Square
3. Rectangle
4. Rhombus
5. Trapezoid
6. Parallelogram
7. Circle (circumference and area)
FIND THE PERIMETER AND AREA OF THE FOLLOWING POLYGONS:
1. A rectangle with a base of 7cm and a height of 4 cm
2. A square whose side measures 9m.
3. A right triangle whose sides measure 3cm, 4cm, and 5cm.
4. A rhombus with diagonals that measure 10m and 26m respectively.
5. An isosceles trapezoid whose legs measure 25cm each, bases 14cm and 16cm long,
and a height that measures 24cm.
6. A rectangle with a base of 8cm and a height of 3 cm
7. A square whose side measures 13m.
8. A right triangle whose sides measure 5cm, 12cm, and 13cm.
9. A rhombus with diagonals that measure 10m and 26m respectively.

5. 10. An isosceles trapezoid whose legs measure 13cm each, bases 14cm and 16cm long,
and a height that measures 12cm.
SOLVE:
1. How many pieces of 2”x2” squares can fit in a rectangle with dimensions 36” x 12”?
2. The sides of a parallelogram are 8 cm and 4 cm. If two adjacent interior angles of
the parallelogram both measure 90  , what is the area of the parallelogram in square
centimeters?
3. A parallelogram has two sides with lengths 18 units and 8 units. The measurement of
one angle is 30  . What is the area of the parallelogram in square units?
4. A square has 12 cm long diagonal. What is its area?
5. The diagonals of a rhombus have lengths 16cm and 30cm. What is the length of a
side of a rhombus in centimeters?
6. The sides of a parallelogram are 16 cm and 4 cm. If two adjacent interior angles of
the parallelogram both measure 90  , what is the area of the parallelogram in square
centimeters?
7. A square has 6 cm long diagonal. What is its area?
8. In a parallelogram ABCD, BC=10 cm and CD = 6cm. If AC is 8cm and AC is
perpendicular to AB, what is the area of ABCD?
9. Both dimensions (length and width) of a rectangular area are doubled, how is the
area changed?
10. A kite is made from two isosceles triangles having a common base as in the figure. If
the lengths of the kite are marked, what is the area of the kite?
11. A trapezoid has parallel sides 13cm and 21cm long. The longer of the two nonparallel
sides is 17, and the shorter is perpendicular to a parallel side. What is the area of the
trapezoid?
12. In the figure, ABCD is a square and the segments forming the boundary of the star are
congruent. Find the area of the star in terms of s and b.

6. Identify if the indicated property is a property of a PARALLELOGRAM, RECTANGLE,
RHOMBUS OR SQUARE.
1. The diagonals bisect each other.
2. The diagonals are congruent.
3. Consecutive angles are congruent.
4. The diagonals bisect the angles of a quadrilateral.
5. The diagonals are congruent and perpendicular.
TRUE OR FALSE:
1. Every square is a rhombus.
2. All squares are rectangles.
3. If the angles of a quadrilateral are congruent, then the quadrilateral is a rectangle.
4. If the diagonals of a quadrilateral are perpendicular bisector of each other, then the
quadrilateral is a rhombus.
5. The sum of the measures of the interior angles of a trapezium is not necessarily 360o
Show your solution in solving for the indicated variables.
BEJO is a parallelogram with diagonals that intersect at point N.
1. BE = 7 x + 6, JO = 9 x + 2 and EJ = 12 x + 1 , find OB.
2. If m∠BEJ = 6 x + 17 and m∠EJO = 9 x − 32, find m∠BOJ .
3. If BJ = 28, BN = 3 x + 2, EN = 7 x − 2, find EO.
4. If BEJO is a rectangle, m∠EBO = 17 x − 12, find x.
5. If BEJO is a square, m∠BOJ = 4 x − 6 and BO = 2 x − 8, find JO.
6. If BEJO is a rhombus, m∠BEO = 12 x − 2 and m∠JEO = 11x + 3 find m∠EJB.
7. If BEJO is a rectangle, BJ = 7 x + 2, EO = 6 x + 5, find NJ .
8. If BEJO is a rhombus, m∠EJB = 32, m∠JBO = 9 x + 5, find m∠BEO.

7. For each part of this problem, answer in the following way:
Write…
“extra” if more information is given than what is needed to get a
numerical answer.
“not enough” if not enough information is given to get a numerical answer.
“ok” if just enough information is given to allow a numerical solution.
“contradicting" if the given information is contradictory.
Note: You do not need to solve, just decide whether or not you can solve
the problems using the given information.
Given that PN is secant and PW is tangent to the circle at point W.
If PW=15 and PA = 50, what is PN?
If PW = 16 what is AN?
Refer to the given figure below:
Given that CD is a diameter of Circle P.
If CF = 4, FP=3 and PD=11, what is CD=?
If AB=12, CD=10, and CF=4, what is PB=?
If AF = 13, CF = 5 and CP = 10, what is CD=?

8. PROPERTIES OF TRAPEZOIDS
A. Given the trapezoid QERY with ER//QY, WT is the median, M is the midpoint of QY. (Rx2)
E R
1. Find WT, if ER=7 and QY=17.
2. Find QY, if WT=13, ER=8. W T
3. Find WT, if ER=12 and QY=17
4. Find QY, if WT=19, ER=8.
5. Find ER, if WT=11 and QY=16.
Q M Y
6. If ER=x+7, WT=2x-1, QY=18, find x, WT and ER.
7. If WT=4x+2, ER=2x-6, QY=8x-4, find x, WT, ER and QY.
8. If QW=3x+5, WE=4x-2, QY=3x+1, WT=2x+5 find the measure of the four segments.
9. Find m∠RYQ , if QERY is an isosceles trapezoid, m∠E + m∠R = 240 .
10. If QERY is an isosceles trapezoid, m∠R = 30, find the measure of the other three angles.
11. Find m∠Q , if QWTY is an isosceles trapezoid, m∠Y = 2 x + 2 and
m∠Q + m∠Y = 5 x − 8 .
12. Find MT if QR=25.
13. Find QR if MT = 16.
adv_math3
quiz305
tangent lines and circles
Solve for what is asked: (rx5)
1. Imagine a circle with center P and radius PQ = 4cm. Locate point A such that PA = 5cm, and a point B such that PB = 2.5 cm.
Complete the following statements:
a) A lies in the _______ of the circle because ___________.
b) B lies in the _______ of the circle because ___________.
c) The circles with radii are called ______.
2. E is a point in the exterior of a circle. How many tangents to the circle contains E?
3. is a radius of the given circle below and is a segment tangent to the circle. If SK = 6 and the diameter of the circle is 18,
how far is point K to the center of the circle?
P
S
K
4. The distance of a point E from the center, A, of a circle is 20. The radius of the circle is 5. A line through E is tangent to the
circle at B. Find EB.
5. Two concentric circles have diameters of 10 and 26. Tangents to the smaller circle pass through the ends of a diameter of the
larger circle. Find the length of the segment along each tangent which has an endpoint on each circle.
I. TRUE OR FALSE
1. The radius of a circle is twice the diameter.
2. Any given segment in a circle can be a radius and at the same time a chord of a circle.

9. 3. If two circles are congruent, then any chord in the first circle is congruent to any chord in the second circle.
4. A secant line can contain a radius of the circle.
5. Two concentric circles have congruent diameters.
II. IDENTIFY IF THE LOCATION OF THE POINT BELOW. TELL WHETHER IT IS IN THE INTERIOR, EXTERIOR OR ON THE CIRCLE.
Given circle M with a radius that measures 5cm.
1. Point N if MN = 6cm
2. Point P if MP = 12cm
3. Point Q if MQ = 14cm
4. Point R if MR = 3cm
5. Point S if MS = 5cm
III. Using the figure at the right, give the appropriate name for each of the following:
1. KL
2. LM n
A
3.
AB
L
T
K
4. n
5. T M
B
IV. Use the given figure to solve for the missing measurements: (2 points each)
11. OR = 12, OP = 13, RP=?
12. OQ = 6, PS = 16, OP=?
13. OR = 12, m∠ROP = 60
OP=?
14. m∠RPS = 150 ,
m∠RPO = ?
15. What kind of triangle is ∆PSR ?
V. Solve for what is asked: (5 points each)
1. CONSTRUCTION: (Use a 1 peso coin and your ID only to draw) Circle A and Circle B are two congruent but non-concentric
circles. The two circles have line CD as the common tangent line with C as the point of tangency of each circle.
2. MATHEMATICAL REASONING: The sentence below contains the word “diameter” twice. Explain how “diameter” is used each
time.
“Although a circle may have only one diameter, a circle actually does have infinitely many diameters”
(PERSEVERANCE, PRUDENCE AND REVERENCE ONLY)
3. E is a point in the exterior of a circle. How many tangents to the circle contains E?
4. is a radius of the given circle below and is a segment tangent to the circle. If SK = 6 and the diameter of the circle is 18,
how far is point K to the center of the circle?
P
S
K
I. For 1-5, solve for the measure of the arcs using the given figure.
1. AEB 2. ADB 3. BE 4. BC 5. EBD

10. II. For each part of this problem, answer in the
following way:
Write “extra” if more information is given that
what is needed to get a numerical answer. Write
“not enough” if not enough information is given. Write “OK” if just enough information is given to allow a
numerical solution.
Note: You do not need to solve, just decide whether or not you can solve the problems using the given information.
Use the figure at the right :
1. CF = 3, FP=2, PD=6, CD=?
2. AB=16, CD=20, CF=4, PB=?
3. CD=30, AB=24, AC=?
4. PB=7, CD=?
5. PF=3, FB=14, PB=?
III. SHOW YOUR SOLUTIONS IN SOLVING FOR WHAT IS ASKED. DRAW A FIGURE IF NONE IS PROVIDED.
SOLUTION/FIGURE: 3 POINTS
CORRECT ANSWER: 2 POINTS
TOTAL POINTS/ITEM: 5POINTS
1. In a circle whose radius is 10cm, a chord is 6cm from the center, how long is the chord?
2. A diameter and a chord of a circle have common endpoint. If the length of the diameter is 40 and the length
of the chord is 24, how far is the chord from the center of the circle?
3. (OPTIONAL) In a circle, a chord 12 cm long is parallel to a tangent and bisects the radius drawn to the point of
tangency. How long is the radius?