No clue how to do this question, please help someone (1 Viewer)

[kpad5991]

 

[jimmysmith560]

Would you be able to include the source of this question? I have tried asking this question elsewhere but unfortunately, my attempt at getting an answer was unsuccessful. The main problem was that people were mostly confused about the wording of the question, i.e. they were unable to determine what the question exactly requires due to its rather "ambiguous" wording. I also saw your post on the Free Math Help forum and have posted a suggestion to your question there (still awaiting moderator approval, likely because it's my first message on that forum, meaning my suggestion may take some time to appear), which I'm not entirely sure of, but I still hope it helps!

 

[Life'sHard]

When I see a question with more than 10 words, I just skip it. When the last sentence of the question, which is suppose to clearly tell you what you're looking for is convoluted, I just skip it. Ceebs man.

 

[kpad5991]

Would you be able to include the source of this question? I have tried asking this question elsewhere but unfortunately, my attempt at getting an answer was unsuccessful. The main problem was that people were mostly confused about the wording of the question, i.e. they were unable to determine what the question exactly requires due to its rather "ambiguous" wording. I also saw your post on the Free Math Help forum and have posted a suggestion to your question there (still awaiting moderator approval, likely because it's my first message on that forum, meaning my suggestion may take some time to appear), which I'm not entirely sure of, but I still hope it helps!

from Math Quest. The answer is 1:2pi
I think they want the area of the small circle to the large circle. But how would you work it out

 

[Eagle Mum]

I'm pretty sure the shaded area P must be relevant.
The ratio of the shaded area P to the area of the smaller circle is 1:2pi (the given solution), but I agree that the question certainly isn't worded to elicit such an answer.

 

[CM_Tutor]

I've reduced the problem to needing to find the value of where is the obtuse angle solution of the equation

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[Eagle Mum]

from Math Quest. The answer is 1:2pi
I think they want the area of the small circle to the large circle. But how would you work it out

I don't think the area of the smaller circle is less than a sixth of the area of the larger circle so the solution 1:2pi cannot be the ratio of the two circles, although I do think solving that as a separate question would be quite interesting. As CM_Tutor has posted, there is a solution that requires one to computationally calculate the angle .

To arrive at the ratio of P to the smaller circle as 1:2pi,

Let the smaller circle be of unit radius,
Its area is then π.
By Pythagoras theorem, half the length of the square’s side is 1/√2 and the length of the whole side is 2/√2 or √2.
The area of the square is therefore 2.

Since each chord cuts the larger circle in the ratio 1:3, each segment is a quarter of the total area (TA) of the larger circle:

Since the segments, with individual area TA/4, overlap at P, the equation summing the areas within the large circle is:

TA = 4x Area of each segment - 4P + Area of the square
TA = 4x(TA/4) - 4P + 2
TA = TA - 4P + 2
4P = 2
P = 1/2

Therefore the ratio of the areas P: small circle = 1/2 : π = 1:2π