CCS2 Honors – Assign 9.4, 9.5, 10.1
Name: ____________________ Per.____
1. Use the given information to answer each question. Justify your answer by giving the name of the theorem
used.
a. If diameter ̅̅̅̅
𝐵𝐷 bisects ̅̅̅̅
𝐴𝐶 , what
b. If diameter ̅̅̅̅
𝐹𝐻 intersects ̅̅̅̅
𝐸𝐺 at a
c. If ̅̅̅̅
𝐾𝑃 ≅ ̅̅̅̅
𝐿𝑁, how does the length
is the angle of intersection?
right angle, how does the length of
̅̅̅
𝐸𝐼 compare to the length of ̅̅̅
𝐼𝐺 ?
̅̅̅̅ compare to the length of 𝑅𝑂
̅̅̅̅?
of 𝑄𝑂
̅̅̅̅ ≅ 𝐻𝑂
̅̅̅̅ and diameter 𝐸𝐽
̅̅̅ is
d. If 𝐺𝑂
̅̅̅̅ is 13
e. If the length of 𝐴𝐵
̅̅̅̅ is 24
f. If the length of 𝐴𝐵
perpendicular to both, what is the
relationship between ̅̅̅̅
𝐺𝐹 and ̅̅̅̅
𝐻𝐾 ?
millimeters, what is the length of
̅̅̅̅
𝐶𝐷?
centimeters, what is the length of
̅̅̅̅
𝐶𝐷?
̅̅̅̅ is 32 inches,
g. If the length of 𝐵𝐹
̅̅̅̅?
what is the length of 𝐶𝐻
h. If the measure of ∠𝐴𝑂𝐵 = 155° ,
i.If TK = 9 mm, KB = 7 mm, VK =
12 mm, find AK.
what is the measure of ∠𝐷𝑂𝐶?
2. a. Draw an inscribed right angle in circle T. Label each point where the angle
intersects the circle. What is the name of the right angle?
b. Draw the chord determined by the inscribed right angle. What is the name of the
chord?
c. What else do you know about the chord determined by an inscribed right angle?
d. Draw a second inscribed right angle in circle T. Label each point where the angle
intersects the circle. What is the name of the second right angle?
e. Draw the chord determined by the second inscribed right angle. What is the name
of the chord?
f. What else do you know about the chord determined by the second inscribed right
angle?
g. Describe the relationship between the arcs that correspond to the chord you
named in parts (b) and (e). Explain your reasoning.
h. Do you think every inscribed right angle will determine the longest chord of the
circle, which is the diameter of the circle? Explain your reasoning.
i. The figure shows a section of a circle. Draw two chords and construct their
perpendicular bisectors to locate the center of the circle.
3. Calculate the measure of each angle. Justify your answer by giving the name of the theorem used.
a. If ̅̅̅̅
𝑂𝐷 is a radius, what is the
̅̅̅̅ is a tangent segment and ̅̅̅̅
b. If 𝑅𝑆
𝑂𝑆 c . If ̅̅̅̅̅
𝑉𝑊 is a tangent segment and
measure of ∠𝑂𝐷𝐶?
is a radius, what is the measure of
∠𝑅𝑂𝑆?
̅̅̅̅ is a radius, what is the measure
𝑂𝑉
of ∠𝑉𝑊𝑂?
d. ⃡𝐺𝐻 and ⃡𝐺𝐼 are tangent to circle
̅̅̅̅
e. Show your work! If ̅̅̅̅
𝐸𝐹 and 𝐺𝐹
are tangent segments, what is the
measure of ∠𝐸𝐺𝐹?
̅̅̅̅̅ and 𝐿𝑀
̅̅̅̅
f. Show your work! If 𝐾𝑀
are tangent segments, what is the
measure of ∠𝐾𝑀𝐿?
O. GH =10 cm, GJ = ?
4. Calculate the length of the segment. Show work!! Give the name of the theorem used.
a. AC = 10, BD = 13, CE = 3,
b. LM = 25, MN = 7, PN = 5,
c. JK = 80, MN = 45, ML = 32,
DE = ?
RP = ?
KL = ?
5. Show work!! Give the name of the theorem used.
a. RS = 15, ST = 5, TU = ?
b. PQ = 4, RQ = 2, SR = ?
d. WV = 36 inches, point X is a
midpoint of segment WV, and YV =
40 inches.
What is YZ?
c. FG = 3, EF = 8, GH = ?
e. Write an equation involving
f. line FG is tangent to circle Q,
the secant the tangent segments. BC = 10 feet, and CG = 4 feet.
What is FG?
6. Draw a triangle inscribed in the circle through the three points. Then determine if the triangle is a right triangle.
a.
b.
c.
d.
7. Draw a triangle inscribed in the circle through the given points. Then determine the measure of the indicated
angle.
a. In ABC, mB = 380,
b. In ABC, mB = 620.
c. In ABC, mC = 490.
Determine mA
Determine mA
Determine mA
8. Draw a quadrilateral inscribed in the circle through the given four points. Then determine the measure of the
indicated angle.
a. In quadrilateral ABCD, mC =
0
b. In quadrilateral ABCD, mB =
c. In quadrilateral ABCD, mB =
75 . Determine mA.
112 . Determine mD.
1010. Determine mD.
9. In the figure shown, RST is
10. Given arc RK= 98°. Show
work!
11. Can we conclude
? with the
following information? Justify
inscribed in circle Q, RS = 18
centimeters, and ST = 24
centimeters. What is RT? Show
work, explain!
0
Arc RZ = ?
Arc ZEK = ?
Angle RUK = ?
Angle ROK = ?
Add segment ZU. Angle ZUK = ?
If angle ERU = 25°, arc EU = ?
If KU = 5, and OK = 6.5, ZU =?