Question

Point C is the center of the circle. Angle ACB measures 49 degrees. What is the measure of arc ADB?

Answer 1

What's your insight on this?

Answer 2

Intuitively you would think that the degree is the same when line is drawn connecting the three points

Answer 3

However after careful scrutiny you would notice that D is indeed not on the straight line

Answer 4

Do you know the radius of the circle?

Answer 5

It would be impossible to determine the length without knowing the radius unless you are talking in ratios.

Answer 6

I'm not really sure, I don't remember the cirlce's unit very well. Is the arc the same as the angle? or doubled? or I could be totally wrong. What I have in the question is all the information I have.

Answer 7

arc is the radian

Answer 8

How do I find that?

Answer 9

\[49 \times \frac{ \pi }{ 180 }\]

Answer 10

but it still doesnt make sense since you dont have the radius or any information of D

Answer 11

So then how do I answer?

Answer 12

what options have you got?

Answer 13

None, this one isn't multiple choice

Answer 14

good luck :)

Answer 15

if the circle has a radius of 1 unit, its something close to pi*radius. thats all i can tell you, sorry

Answer 16

It doesn't tell me the radius or diameter at all... Thanks anyway

Answer 17

Use the formula
\[l=r.\theta\]
where l is arc length, r is radius and theta is the angle subtended(measured in radians)
clearly r is constant for a given circle so
\[l_{1}=r.\theta_{1}\]
and
\[l_{2}=r.\theta_{2}\]\[\frac{l_{2}}{l_{1}}=\frac{\theta_{2}}{\theta_{1}}\]
Using this we can calculate for arc length
\[l_{2}=\frac{\theta_{2}}{\theta_{1}}.l_{1}\]
Now you are neither given l1 nor theta 2, although one would think theta 2 is 180 degrees, it could be wrong, is there more information given in the question??

Answer 18

You don't need to convert to radians here though, if u just use degrees for both angles u'll be fine as their units cancel out

Answer 19

No, that's it, thats all I was given

Answer 20

Then there is definitely some information missing in the question I think, it is incomplete.

Answer 21

I'm just looking for the arc length, is there no way to get that from this information? I thought I just needed to find the length of AB then subtract that from 180 and the rest was ADB. But I can't solve for AB without the radius?

Answer 22

Or I'm completely wrong... I can just skip this one, if it cant be solved

Answer 23

I meant 360, not 180**

Answer 24

I'll just skip this one I guess, thank ya'll anyway

Answer 25

If it is asking for the degree measure of the arc, it is equal to the central angle measure of the circle.

Answer 26

I'm guessing that A, C, and D are supposed to be in a straight line.

Answer 27

@K.Binks

Answer 28

Any ideas using that info?

Answer 29

How do I solve for the arc measure that way? The whole circle equals 360, I'm given the arc AB, which is 49 (right?) and they're looking for arc ADB, so just 360-49= 311.. right? @JoannaBlackwelder

Answer 30

Yep, perfect!