# Finding missing measures within a circle

#### Qwo127

##### New member
I’m really confused on how to find the rest of these measures...

#### pka

##### Elite Member
I’m really confused on how to find the rest of these measures...View attachment 17430
It is not at all clear to me what some of your variables are? i.e. what is $$u~?$$
It is clear that $$m(\angle AIB)=49^o$$ is that $$u~?$$
Why do you have $$m(\widehat{IV})=24^o~?$$

#### Qwo127

##### New member
u is an angle that needs to be found and it would angle BAI, in terms of points on the circle, and I have (IV) as 24 because IE is congruent to IV. The total measure of IE is 12+12 = 24 , so then since IE and IV are equal then they are both 24.

#### pka

##### Elite Member
u is an angle that needs to be found and it would angle BAI, in terms of points on the circle, and I have (IV) as 24 because IE is congruent to IV. The total measure of IE is 12+12 = 24 , so then since IE and IV are equal then they are both 24.
Good enough.
$$m(\widehat{IX})=49^o$$
$$m(\widehat{XEN})=131^o$$
$$m(\widehat{VN})=180^o-m(\widehat{IV})$$

#### Qwo127

##### New member
How about the measure of angle C? And, do you agree that arc (IV) is 24?

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#### Qwo127

##### New member
Can you just subtract 360-90-131-108 = 31 which is angle C since you have 3 out of the 4 angles in the quadrilateral AXFC?

#### Jomo

##### Elite Member
IE is 12+12 = 24 , so then since IE and IV are equal then they are both 24. This is true, but the question is what is 24. The answer is the length of IE is 24. You were ask for the arc length of IV

#### Qwo127

##### New member
IE is 12+12 = 24 , so then since IE and IV are equal then they are both 24. This is true, but the question is what is 24. The answer is the length of IE is 24. You were ask for the arc length of IV
So, the arc length of IV is not equivalent to its length? So, if its not 24 how do you find the length? But, yes, I’m trying to find the arc length of IV.

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#### Jomo

##### Elite Member
Doesn't the arc length look longer? Have you ever heard that the shortest distance between two points is a straight line?

Seriously, if you had to walk from I to V and was in a very big rush would you walk along the line or the arc? Please assume the rate at which you walk will be the same.

#### Qwo127

##### New member
Doesn't the arc length look longer? Have you ever heard that the shortest distance between two points is a straight line?

Seriously, if you had to walk from I to V and was in a very big rush would you walk along the line or the arc? Please assume the rate at which you walk will be the same.
So you’re saying it’s still the same distance, hence the same length, meaning the arc of IV is 24?

But that wouldn’t make sense right because Arc XE is 49 and it looks smaller.

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#### Jomo

##### Elite Member
So you’re saying it’s still the same distance, hence the same length, meaning the arc of IV is 24?

But that wouldn’t make sense right because Arc XE is 49 and it looks smaller.
Just because you and I for example walk from point I to point V does not mean we walked the same distance. Maybe I took the long way.

Consider this. There is round track (for running). We are 180o apart. That weans if you drew a line between us it would go through the center of the track. If you wanted to walk over to me would it be shorter to walk along the diameter, walk around half the circular track orit doesn't matter?

#### Qwo127

##### New member
Just because you and I for example walk from point I to point V does not mean we walked the same distance. Maybe I took the long way.

Consider this. There is round track (for running). We are 180o apart. That weans if you drew a line between us it would go through the center of the track. If you wanted to walk over to me would it be shorter to walk along the diameter, walk around half the circular track orit doesn't matter?
Walking along the diameter, so in that case it is not 24. So, how do I find it without knowing the arc of VN?

#### pka

##### Elite Member
How about the measure of angle C?
The angle in question is the result of a tangent & a secant of a circle.

The measure of such an angle is one half the measures of the major intercepted arc minus the minor intercepted arc.

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#### Qwo127

##### New member
The angle in question is the result of a tangent & a secant of a circle.

The measure of such an angle is one half the measures of the major intercepted arc minus the minor intercepted arc.
So, the major intercepted arc is 131 and the minor is 49? So the answer is 41?

Or, is it 98-82/2 = 8? The 41 seems more reasonable.

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#### Qwo127

##### New member
I’m still confused on whether or not I’m doing this correctly.

#### Qwo127

##### New member
The angle in question is the result of a tangent & a secant of a circle.

The measure of such an angle is one half the measures of the major intercepted arc minus the minor intercepted arc.
So, if the answer is 41 = 131-49/2, then where do you start to find the arc of IV and arc of VN? I just want to start on the right track.

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#### Qwo127

##### New member
Could anyone check my updated answers to see if I’m on the right track and if these are correct?

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#### Jomo

##### Elite Member
So, if the answer is 41 = 131-49/2, then where do you start to find the arc of IV and arc of VN? I just want to start on the right track.
41 is an integer. 131 is an integer. 49/2 is not an integer nor can it be written as one. After all, an odd number, like 49, can not be evenly divided by 2. That is what makes an integer odd. Now how can 131 - 49/2 (ie 131 - 25.5) equal an integer?

#### Qwo127

##### New member
41 is an integer. 131 is an integer. 49/2 is not an integer nor can it be written as one. After all, an odd number, like 49, can not be evenly divided by 2. That is what makes an integer odd. Now how can 131 - 49/2 (ie 131 - 25.5) equal an integer?
Sorry, you would subtract 131-49, first, then divide them by 2 which gives you 41. But, is this correct in terms of angle C? Or, can you just subtract 360-90-131-108 = 31 which is angle C since you have 3 out of the 4 angles in the quadrilateral AXFC?

#### Jomo

##### Elite Member
Sorry, you would subtract 131-49, first, then divide them by 2 which gives you 41. But, is this correct in terms of angle C? Or, can you just subtract 360-90-131-108 = 31 which is angle C since you have 3 out of the 4 angles in the quadrilateral AXFC?
This is why you need to use parenthesis. I could have responded to a different post instead of your post. Please just write 41 = (131-49)/2