CCS2 Honors – Assign 9.4, 9.5, 10.1
Name: ____________________ Per.____
1. Use the given information to answer each question.
̅̅̅̅ , what
̅̅̅̅ bisects 𝐴𝐶
a. If diameter 𝐵𝐷
̅̅̅̅ intersects ̅̅̅̅
b. If diameter 𝐹𝐻
𝐸𝐺 at a
is the measure of the angle of
intersection?
right angle, how does the length of
̅̅̅
𝐸𝐼 compare to the length of ̅̅̅
𝐼𝐺 ?
of ̅̅̅̅
𝑄𝑂 compare to the length of
̅̅̅̅
𝑅𝑂?
̅̅̅̅ ≅ 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 =
i.If TK = 9 mm, KB = 7 mm, VK =
12 mm, find AK.
°
155 , what is the measure of
∠𝐷𝑂𝐶?
̅̅̅̅ ≅ 𝐿𝑁
̅̅̅̅, how does the length
c. If 𝐾𝑃
2. a. Draw an inscribed right angle in circle T. Label the points where the angle
intersects the circle A, B, C.
b. Draw the chord determined by the inscribed right angle.
c. What is another name for the chord determined by an inscribed right angle?
d. Draw a second inscribed right angle in circle T. Label the points where the
angle meets the circle D, E, F.
e. Draw the chord determined by the second inscribed right angle.
f. Describe the relationship between the arcs that correspond to chords AC and DF.
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. Label this center point A.
3. Calculate the measure of each angle. Show work where appropriate!
̅̅̅̅ is a radius, what is the
a. If 𝑂𝐷
̅̅̅̅ is a tangent segment and
b. If 𝑅𝑆
̅̅̅̅̅ is a tangent segment and
c . If 𝑉𝑊
⃡ and 𝐺𝐼
⃡ are tangent to circle
d. 𝐺𝐻
e. Show your work! If ̅̅̅̅
𝐸𝐹 and ̅̅̅̅
𝐺𝐹
are tangent segments, what is the
measure of ∠𝐸𝐺𝐹?
f. Show your work! If ̅̅̅̅̅
𝐾𝑀 and ̅̅̅̅
𝐿𝑀
are tangent segments, what is the
measure of ∠𝐾𝑀𝐿?
measure of ∠𝑂𝐷𝐶?
O. GH =10 cm, GJ = ?
̅̅̅̅
𝑂𝑆 is a radius, what is the measure
of ∠𝑅𝑂𝑆?
̅̅̅̅
𝑂𝑉 is a radius, what is the measure
of ∠𝑉𝑊𝑂?
4. Calculate the length of the segment. Show work!!
a. AC = 10, BD = 13, CE = 3,
b. LM = 25, MN = 7, PN = 5,
DE = ?
RP = ?
c. JK = 80, MN = 45, ML = 32,
KL = ?
5. Show work!!
a. RS = 15, ST = 5, TU = ?
b. PQ = 4, RQ = 2, SR = ?
c. FG = 3, EF = 8, GH = ?
e. Write an equation involving
the secant the tangent
segments.
f. line FG is tangent to circle Q,
d. WV = 36 inches, point X is a
midpoint of segment WV, and YV =
40 inches.
What is YZ?
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 find 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 find the measure of the angle.
a. In quadrilateral ABCD, mC =
b. In quadrilateral ABCD, mB = c. In quadrilateral ABCD, mB =
750. Determine mA.
1120. Determine mD.
1010. Determine mD.
9. In the figure shown, RST is
10. Given arc RK= 98°. Show
work!
11. Prove
Given:
inscribed in circle Q, RS = 18
centimeters, and ST = 24
centimeters. What is RT? Show
work, explain!
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 =?
12. Find the trig ratios:
5𝜋
a. 𝑠𝑖𝑛 4 =
b. 𝑡𝑎𝑛
3𝜋
2
=
13. Find the angle (No calc.)
1
a. 𝑠𝑖𝑛𝐴 = 2
b. 𝑠𝑒𝑐𝐵 = −√2
14. Write the equation of a line
that passes through (-3, 0) and is
parallel to 2𝑥 − 4𝑦 = 8