# Maths help!

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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.

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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(Original post by

is this from a actual question paper?

**tinygirl96**)is this from a actual question paper?

https://imgur.com/a/nscsrzZ

Here is the explanation if you were curious.

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#4

(Original post by

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.

**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.

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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(Original post by

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.

**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.

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#6

(Original post by

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.

**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.

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