Question

Inscribed Angle help! @e.mccormick

Answer 1

Ok, so, where is the angle?

Answer 2

Line AB is tangent to circle O at B. Find the length of the radius r for AB = 8 and AO = 11.7. Round to the nearest tenth if necessary. The diagram is not to scale.

Answer 3

I know we have to use the pithagorian theorum.

Answer 4

a^2+b^2=c^2 but I dont know which order the numbers go in...

Answer 5

Because AB is tangent, yes, you can use pythagorus. Now, in that C is the Hypotenuse. That help? Or need a little more?

Answer 6

Let me check

Answer 7

Also, the tangent means that the angle at B is the right angle.

Answer 8

C= AO?

Answer 9

Yah.

Answer 10

What are the other two angles called? I can't remember their names. Hypotenus and the other two? Once I know their names I can plug them into the equation. But for some reason I cannot think of them lol.

Answer 11

they just call the other sides the legs.

Answer 12

The angles opposite them have no special names... other than they are acute because it is a right triangle.

Answer 13

Oh. so it doesn't matter which one is a or b?

Answer 14

Exactly.

Answer 15

Is this right?: 8^2+r^2=11.7^2

Answer 16

Then I just simplify?

Answer 17

Well, solve for r.

Answer 18

64+r^2=136.89

Answer 19

I got r=8.5?

Answer 20

Yah, that is rounded to 1 decimal.

Answer 21

Lol yeah, they asked for the nearest tenth.

Answer 22

Yep. So that works.

Answer 23

Would you mind helping me with another problem?

Answer 24

Sure, what is it?

Answer 25

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

Answer 26

Do you see where the right triangle is hiding that exposes the measure of all radii?

Answer 27

I see the right angle, yeah.

Answer 28

Add a line to make the right triangle. That will be the hypotenuse you need to solve for.

Answer 29

Okay, so: 9^2+6^2=x^2?

Answer 30

whoops i mean 12^2 instead of the 6^2

Answer 31

because that line on the top of the circle is broken into half, and since one side is 12, the other side is also 12. Right?

Answer 32

81+144=x^2
225=x^2
Then I square rooted both to get 15=x

Answer 33

Okay, so those ones are getting easier for me. But there's these other ones I have to do and they look difficult.

Answer 34

I am thinking they gave you \(12^2+9^2=?^2\) because visuially it does liik that way. So yah, 15.

Answer 35

I really appriciate you helping me, that last time you helped me I got a 98% on my test.

Answer 36

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

Answer 37

x would equal 40 right? because they are congruent?

Answer 38

hello?

Answer 39

Had a bit of lag there... fun connection at times.

Dude, did you read the Code of Conduct for the site?
http://openstudy.com/code-of-conduct

One of the things they are against is things that "...violates your school's Honor Code..." like getting someone to help you with a test.

Answer 40

No you didn't help me with a test. You helped me do good on the test. Like, you helped me understand how to do a certain problem that was going to be on the test.

Answer 41

OH, I see.. you meant last time... Aaaah... Kk. That makes more sense now,. Sorry bout that.

Answer 42

There have been a rash of people posting test questions recently. Not at all good.

Answer 43

yes, they would be congruent, so 40%.

Answer 44

Lol, no problem. I don't see the point in cheat because it won't help in the long run.

Answer 45

This is just a worksheet that get assigned to BEFORE the actual test. They don't explain it very well for me to understand, so I found this site and its helped so far!

Answer 46

Yah. There was this sign in an engineering department someone posted to the web, "If you get the calculation wrong in real life, people die. So don't cheat and learn the material!"

Answer 47

Lol yeah. I have 4 more problems then Ill be good to go. Can you help me with them still? Or are you busy?

Answer 48

Sure. Fire away.

Answer 49

Awesome. Thank you.

Answer 50

Find the value of x. If necessary, round your answer to the nearest tenth. The figure is not drawn to scale.

Answer 51

Hmmm.... have any other info?

Answer 52

FG = 20, RS = 24, OP = 14

Answer 53

OK, with OP and half of FG, you can get r. That make sense?

Answer 54

I make it into a triangle again?

Answer 55

Yep!

Answer 56

And once you have r, that can solve the other triangle for OQ or x.

Answer 57

I got 17.2 for r

Answer 58

yah

Answer 59

I got 12.3 for x!

Answer 60

Does that upside down T symbol mean intersect?

Answer 61

Perpendicular.

Answer 62

Oh okay.

Answer 63

And inside a circle, things that are perpendicular to a chord and go through the center, well, they bisect the chord.

Answer 64

and make a 90 degree angle

Answer 65

yes, which is why the right triangle laws can take over.

Answer 66

so \(2\sqrt{38}\approx 12.3\) is great there.

Answer 67

Oh okay.

Answer 68

Ready for the next one? It looks different from the ones we've been doing..

Answer 69

Sure.

Answer 70

Use the diagram. Line AB is a diameter, and Line AB is perpendicular to Line CD . The figure is not drawn to scale.

Answer 71

Then it says find mBD for mAC=58 degrees.

Answer 72

Instead of a line above the letters, it's like a curved line

Answer 73

Arch I think.

Answer 74

Yes, the arc.

Answer 75

OK.... a couple ways to take this on, but, the best start is that you look at this, and with the perpendicular lines, you have an inscribed kite, right?

Answer 76

Yeah, a kite.

Answer 77

Do you remember the rules about what is similar in angles in kites, side lengths, etc?

Answer 78

No...

Answer 79

The only thing I think I remember would be that the two triangles on the bottom are congruent and the ones on the top are congruent also.

Answer 80

and the angles are equal when they are diagonally across from each other, right?

Answer 81

Ah, OK... that is the key to this. because AB is a diameter and perpendicular to CD, we know it is a kite where CP=CD. Because of that, AC=AD. Well, this translates to the arcs inscribing the kite as well!

Answer 82

Okay, so AC and AD both are 58 degrees

Answer 83

Yes, which tells you how much about the rest of the circle?

Answer 84

Circle is 360 degrees so I would add 58+58 and get 116 degrees. Then 360-116=244 degrees?

Answer 85

Yes. The other half is 244.... and the large part of the kite also has equal pieces, so each is half that remainging value.

Answer 86

Half of 244?

Answer 87

122?

Answer 88

So, CB=DB?

Answer 89

Yay. that would be it!

Answer 90

Haha, cool! That was pretty easy.

Answer 91

Once you find one side, you can find the others.

Answer 92

Okay, 2 more!

Answer 93

Find the measure of angle BAC. The figure is not drawn to scale.