dacool1:
Answer is 7
Since the chords are enclosed to form a cyclic polygon and are of lengths 1,2,3,5,7,11,13
Angle at center =360
Ratio of angles =1:2:3:5:7:11:13
Sum of ratio =42
Working with chord 7
Angle subtended by chord 7 =7/42 *360
ANGLE = 60
Length of chord =2rsin®/2
7=2rsin30
R=7/2sin30
R=7

Nice try but this rule only applies to regular polygons.

Mitocyan:


Smart method but not cool. I was a bit shocked that you resorted to trial and error and this makes the problem less interesting. This method can work for any polygon with sides of arbitrary length and you made it look like we were supposed to use a property of prime numbers to arrive at the solution.

There is litrary no know way to do summation of more than three trigonometry inverse,
I was expecting someone to point that out.
The prime relationship is only on the length of the chord,

Mitocyan:


Nice try but this rule only applies to regular polygons.

It is wrong

THIS forum is for news and happenings and not maths forum abeg

Can you take a picture of the solution

R=7

ericmor:

Na so my brother, but next time make u just take the number before which is 7 and put . Anything eg, 7.3, 7.4, 7.5 Who get time as no time to waste time. If dem like make dem wrong am, e no kuku comot or add one naira to my pocket

lol

Mrshape:

Let the anglees subtended at the center of each sector
by the perpendicular line draw from the circle centre
@1,@2,@3,@4,@5,@6
@1+@2+@3+@4+@5+@6=180
Sin^-1(1/R) +sin^-1(1.5/R)+sin^-1(2.5/R)+sin^-1 (3.5/R)
+sin^-1 (5.5/R)+sin^-1 (6.5/R)=180
The substitute values into R to check which is the
closest to 180° note you should start from values grater
than 6.5 because height of the longest chord
h=√(R^2-6.5^2)
Note walfrom aphal can't even compute that and get
numerical values, so only substitution works or graph it
Thus R =7.4233units. Look forward to my next shape, I remain Mr shape your shape lover,

Oga Ifada na u be this?

Next prime number = diameter. Next prime number = 17 Diameter = 17 Radius = 17/2 R= 8.5

your solution seems wrong though. since you worked with the sector and each arc of each sector is directly proportional to the angle subtended at the centre of the circle. thus the length of the chords have a relationship with the angles thus making a ratio out of it.

Timmyspy:
Next prime number = diameter.
Next prime number = 17
Diameter = 17
Radius = 17/2
R= 8.5

This your solution does not have leg

Op wait make ivsolve am

MrShape is absolutely wrong . The only person that got it right is Dacool1 . Dacool1 deserves an applause

dacool1:
your solution seems wrong though. since you worked with the sector and each arc of each sector is directly proportional to the angle subtended at the centre of the circle. thus the length of the chords have a relationship with the angles thus making a ratio out of it.

You're very much on point brov .

Mrshape:

Let the anglees subtended at the center of each sector

by the perpendicular line draw from the circle centre

@1,@2,@3,@4,@5,@6

@1+@2+@3+@4+@5+@6=180

Sin^-1(1/R) +sin^-1(1.5/R)+sin^-1(2.5/R)+sin^-1 (3.5/R)

+sin^-1 (5.5/R)+sin^-1 (6.5/R)=180

The substitute values into R to check which is the

closest to 180° note you should start from values grater

than 6.5 because height of the longest chord

h=√(R^-6.5)

Note walfrom aphal can't even compute that and get

numerical values, so only substitution works or graph it

Thus R =7.4233units.
Look forward to my next shape, I remain Mr shape your shape lover,

This solution is wrong . The question is not as complex as u made it seems . Dacool1's solution is straight on point . U can apply his method for both regular and irregular polygon inscribe in a circle. Cheers

Solution

EazyGiant:
Solution

Sorry but how did you get the angles in the first place?

EazyGiant:
Solution

how did you get the angles?

Darivie04:

Sorry but how did you get the angles in the first place?

Use the same method to calculate the angles subtended by respective chords

Tonylyte:





Oga Ifada na u be this?

Yes oga slim we done carry shape come hare o

EazyGiant:
Use the same method to calculate the angles subtended by respective chords

This is wrong for irregular polygon my proof
L=2R sin(@/2)
R=5/(2sin(@/2))
R=5/(2sin(42.86/2))
R=2.5/sin(21.43)
R=6.842487

That is how all the radius of the different sector will be different, which is not true for a circle,
In a circle all radius at any point is equal.
Thus my solution is very correct,
I remain Mr Shape

EazyGiant:
Solution

This is wrong for irregular polygon my proof
L=2R sin(@/2)
R=5/(2sin(@/2))
R=5/(2sin(42.86/2))
R=2.5/sin(21.43)
R=6.842487

That is how all the radius of the different sector will be different, which is not true for a circle,
In a circle all radius at any point is equal.
Thus my solution is very correct,
I remain Mr Shape

EazyGiant:
This solution is wrong . The question is not as complex as u made it seems . Dacool1's solution is straight on point . U can apply his method for both regular and irregular polygon inscribe in a circle. Cheers

That's not true
Proof
The got 7
Let me use the chord length of 5

This is wrong for irregular polygon my proof
L=2R sin(@/2)
R=5/(2sin(@/2))
R=5/(2sin(42.86/2))
R=2.5/sin(21.43)
R=6.842487

That is how all the radius of the different sector will be different, which is not true for a circle,
In a circle all radius at any point is equal.
Thus my solution is very correct,
I remain Mr Shape

EazyGiant:
MrShape is absolutely wrong . The only person that got it right is Dacool1 . Dacool1 deserves an applause

I am very correct proof.
You guys got 7
Let me use the chord length of 5

This is wrong for irregular polygon my proof
L=2R sin(@/2)
R=5/(2sin(@/2))
R=5/(2sin(42.86/2))
R=2.5/sin(21.43)
R=6.842487

That is how all the radius of the different sector will be different, which is not true for a circle,
In a circle all radius at any point is equal.
Thus my solution is very correct,
I remain Mr Shape

Mrshape:

I am very correct proof.
You guys got 7
Let me use the chord length of 5

This is wrong for irregular polygon my proof
L=2R sin(@/2)
R=5/(2sin(@/2))
R=5/(2sin(42.86/2))
R=2.5/sin(21.43)
R=6.842487

That is how all the radius of the different sector will be different, which is not true for a circle,
In a circle all radius at any point is equal.
Thus my solution is very correct,
I remain Mr Shape

There will be different values of " R " becos the polygon is irregular . The substended angle with respect to each arc / chord will determine the particular " R " in question . Definite method , not trial and error Sir . I have 2 questions for U ... 1). Do you agree with the substended angles stated above for each arc / chord ? If u disagree , make ur calculation and let's see . 2). Is the 7.42 u got for R the same for all the Rs in the Polygon ?

EazyGiant:
There will be different values of " R " becos the polygon is irregular . The substended angle with respect to each arc / chord will determine the particular " R " in question . Definite method , not trial and error Sir . I have 2 questions for U ... 1). Do you agree with the substended angles stated above for each arc / chord ? If u disagree , make ur calculation and let's see . 2). Is the 7.42 u got for R the same for all the Rs in the Polygon ?

Irrespective of regular or irregular polygon inscribed in a circle the radius of the circle does not change it is a constant.
(1)I agree to your ratio of( lenght of arc/total lenght of chord ) x360 for only regular polygon to get angle subtended,
But this polygon is irregular, so I don't agree with your usage of this formula here it does not apply to irregular polygon
(2) yes the 4.2... I got for R is same for all R in the entire circle.
Hope you are convinced by this.

Check on my new shape and give it a trial sir

Mrshape:
Yes oga slim we done carry shape come hare o

Yes ooo, every shape must be solve.

Mrshape:

Irrespective of regular or irregular polygon inscribed in a circle the radius of the circle does not change it is a constant.
(1)I agree to your ratio of( lenght of arc/total lenght of chord ) x360 for only regular polygon to get angle subtended,
But this polygon is irregular, so I don't agree with your usage of this formula here it does not apply to irregular polygon
(2) yes the 4.2... I got for R is same for all R in the entire circle.
Hope you are convinced by this.

Check on my new shape and give it a trial sir

Length of chord/total length of chords x 360

Or length of arc/total lenght of chord x 360?

Tonylyte:




Length of chord/total length of chords x 360

Or length of arc/total lenght of chord x 360?

Yes but arc lenght is not given, thus second formula don't apply here

Mitocyan:


Smart method but not cool. I was a bit shocked that you resorted to trial and error and this makes the problem less interesting. This method can work for any polygon with sides of arbitrary length and you made it look like we were supposed to use a property of prime numbers to arrive at the solution.

Exactly my thought

tharealest:


Exactly my thought

If you check my first few comments I stated that u should not base your mind on prime number, the prime number is just for the length of chord,
Check my other shapes and give it a trial

Mrshape:
Yes but arc lenght is not given, thus second formula don't apply here

Boss!