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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 ?

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

Solution

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

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