Circles Quiz Study Guide
Geometry
1) What is x?
2) Swimming Pool You are standing 36 feet from a
circular swimming pool. The distance from you
to a point of tangency on the pool is 48 feet as
shown. What is the radius of the pool?
3) Find x.
̂?
4) What is 𝑚𝐷𝐴𝐵
̂.
5) Find 𝑚𝐵𝐶
Use F for #6-14 to determine whether the given arc is a minor arc, major arc, or semicircle. Then, give the
measure of the arc.
̂
6) 𝑚𝑃𝑄
̂
7) 𝑚𝑆𝑇
̂
8) 𝑚𝑇𝑃𝑆
̂
9) 𝑚𝑅𝑇
̂
10) 𝑚𝑅𝑄𝑆
̂
11) 𝑚𝑄𝑅
̂
12) 𝑚𝑃𝑄𝑆
̂
13) 𝑚𝑇𝑄𝑅
̂
14) 𝑚𝑃𝑆
In 15 – 16, determine whether the given arcs are congruent.
̂
̂ 𝑎𝑛𝑑 𝐶𝐷
̂
̂ 𝑎𝑛𝑑 𝑄𝑅
15) 𝐽𝐾
16) 𝐴𝐵
̂.
17) Find 𝑚𝐿𝑀
̂.
18) Find 𝑚𝑃𝑄𝑅
̂.
19) Find 𝑚𝐾𝐿𝑀
20) Find x.
21) Find x.
̂.
22) Find 𝑚𝑆𝑇
̂.
23) Find 𝑚𝐴𝐵
24) mK
25) What is x and y?
26) What is x?
27) If WA is tangent to the circle
28) If mAEC  110 and
29) If mPN  ( x 2 ) , mQR  (11x)
at point W and mWVX  268 ,
find mAWX
mAC  75 , find mBD .
30) Given: Quadrilateral ABCD is inscribed in Circle O.
Prove: ∠𝐵 ≅ ∠𝐴𝐷𝐸
and mPTN  (9 x  4) ,
find the value of x.