noname900
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https://imgur.com/a/4HbQTLO

I'm not sure as to what the question is asking. I initially thought that the largest point would be when PQR form a tangent and would be at pi radians. But 3 answers give pi for the area when I put pi into the option.
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tinygirl96
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is this from a actual question paper?
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noname900
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(Original post by tinygirl96)
is this from a actual question paper?
It's a question from the MAT. I was confused as to what they wanted, but once I got it through my head that they wanted a general formula for any theta, it was do-able. Also if you have done polar coordinates, apparently you're supposed to know it was b.

https://imgur.com/a/nscsrzZ

Here is the explanation if you were curious.
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mqb2766
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(Original post by noname900)
https://imgur.com/a/4HbQTLO

I'm not sure as to what the question is asking. I initially thought that the largest point would be when PQR form a tangent and would be at pi radians. But 3 answers give pi for the area when I put pi into the option.
I think you know that they're asking for a maximum area formula when the points, Q,R, are suitably placed for a given angle theta at P. The formula itself will be maximum when the shaded area approaches the whole circle and theta goes to pi rad.

So the problems are
1) What is the point placement, Q,R, which gives maximum area?
2) What is the formula?
Your attached mark scheme answers the 2nd using a circle theorem construction and hints that the first must be true when the two chords PQ, PR have equal length. You can do a very simple argument by rotating Q,R slightly, keeping that a constant, and noting the area gained/lost will depend on the chord length. For both chords, the net area gained is zero when both are the same length.
Last edited by mqb2766; 1 month ago
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noname900
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(Original post by mqb2766)
I think you know that they're asking for a maximum area formula when the points, Q,R, are suitably placed for a given angle theta at P. The formula itself will be maximum when the shaded area approaches the whole circle and theta goes to pi rad.

So the problems are
1) What is the point placement, Q,R, which gives maximum area?
2) What is the formula?
Your attached mark scheme answers the 2nd using a circle theorem construction and hints that the first must be true when the two chords PQ, PR have equal length. You can do a very simple argument by rotating Q,R slightly, keeping that a constant, and noting the area gained/lost will depend on the chord length. For both chords, the net area gained is zero when both are the same length.
Yea, I understood it after and was able to derive the right option. Initially, I just went to thinking that the greatest area would be when pqr form a tangent, and then had no clue after that as to how they got the formula. But it makes a whole lot of sense getting that they want a general formula for any angle theta, because then I can start asking myself the right questions. As in when the area would be the greatest with any theta, using intuition and then thinking how to calculate the area of pqr.
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mqb2766
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(Original post by noname900)
Yea, I understood it after and was able to derive the right option. Initially, I just went to thinking that the greatest area would be when pqr form a tangent, and then had no clue after that as to how they got the formula. But it makes a whole lot of sense getting that they want a general formula for any angle theta, because then I can start asking myself the right questions. As in when the area would be the greatest with any theta, using intuition and then thinking how to calculate the area of pqr.
Sounds like you adopted a good problem solving strategy for working it out.
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