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Name: _____________________________________________________________
Date: _________________________
Chapter 13: Circle Arcs & Angles
Topic 1: Angle Relationships – Central & Inscribed – Day 2
Period: ______
Have out your notes from yesterday. ALL students in each group must participate in order to receive credit.
1. AB is a diameter of the circle shown. The radius is 12.5 cm, and AC=7 cm. What is the length of BC?
2. In the figure below, AB is the diameter of a circle of radius 17 miles. If BC=30 miles, what is AC?
3. In the figure, BCDE is a rectangle inscribed in circle A. DE=8, BE=15. Find AE (not drawn).
4. In circle A, the measure of angle D is 25°. Find the measure of x. Justify each step along the way.
Homework: Check your answers online. Quiz tomorrow! Be ready!
Name: _____________________________________________________________
Date: _________________________
Period: ______
5. In circle A, the measure of angle D is 15°. Find the measure of x. Justify each step along the way.
6. In circle A, the measure of angle B is 32°. Find the measure of x. Justify each step along the way.
7. In circle A, the measure of angle D is 19°. Find the measure of x. Justify each step along the way.
8. Toby says ∆𝐵𝐸𝐴 is a right triangle because ∠𝐵𝐸𝐴 = 90°. Is he correct? Justify your answer to him.
Homework: Check your answers online. Quiz tomorrow! Be ready!
Name: _____________________________________________________________
Date: _________________________
Period: ______
Answers:
1) <C=900 (Inscribed angles)
BC=24 (Pythagorean Theorem)
2) <C=900 (Inscribed angles)
AC=16 (Pythagorean Theorem)
3) Rectangle: opposite sides are congruent, diagonals bisect each other, right angles
CE=17
AE=8.5
̂ =500 (Inscribed angles)
4) 𝐵𝐶
x=500 (Central angles)
̂ ̂=300 (Inscribed angles)
5) 𝐵𝐶
<BAC=300 (Central angles)
<CAD=1500 (Supplementary angles)
ACD is an isosceles triangle because radii are congruent
x+x+150=180 (All triangle angles = 1800)
x=150
OR
ACD is an isosceles triangle because radii are congruent
<C≅<D (base angles are congruent)
<C=150
6) Arc CD=640 (Inscribed angles)
<CAD=640 (Central angles)
ACD is isosceles triangle because radii are congruent
x+x+64=180 (All triangle angles = 1800)
x=580
7) Arc CD=380 (Inscribed angles)
<CAD=380 (Central angles)
ACD is isosceles triangle because radii are congruent
x+x+38=180 (All triangle angles = 1800)
x=710
8) Arc BD=700 (Central Angles)
<C=350 (Inscribed angles)
50+35+<DEC=180 (All triangle angles = 1800)
<DEC=950
<BEA=950 (Vertical angles are congruent)
Homework: Check your answers online. Quiz tomorrow! Be ready!