http://www.ck12.org Chapter 9. Circles
- First find the radius. In the picture,ABis a radius, so we can use the right triangle 4 ABC, such thatABis the
hypotenuse. From Chord Theorem #3,BC=6.
32 + 62 =AB^2
9 + 36 =AB^2
AB=
√
45 = 3
√
5
In order to findmBD̂, we need the corresponding central angle,^6 BAD. We can find half of^6 BADbecause it is an
acute angle in 4 ABC. Then, multiply the measure by 2 formBD̂.
tan−^1(
6
3
)
=m^6 BACm^6 BAC≈ 63. 43 ◦This means thatm^6 BAD≈ 126. 9 ◦andmBD̂≈ 126. 9 ◦as well.
Practice
Find the value of the indicated arc in
⊙
A.
1.mBĈ
2.mBD̂
3.mBĈ
4.mBD̂
5.mBD̂
6.mBD̂Algebra ConnectionFind the value ofxand/ory.
7.
8.
9.
10.AB= 32
11.
12.
13.
14.
15.- FindmAB̂in Question 10. Round your answer to the nearest tenth of a degree.
- FindmAB̂in Question 15. Round your answer to the nearest tenth of a degree.
In problems 18-20, what can you conclude about the picture? State a theorem that justifies your answer. You may
assume thatAis the center of the circle.
18.
19.
20.