Lesson: Circles

Comment on Circles

These questions from the related resources,I solved the first question using π as 3, to get a circumference of 15, which makes quantity A and quantity B equal,hence option C.but the solution provided on the GRE Prep club, put the solution as quantity A being greater.Is this the correct solution to the problem?
greenlight-admin's picture

You're referring to this question: http://greprepclub.com/forum/a-circle-is-inscribed-in-a-square-with-side...

You got answer answer of C because you plugged in 3 for pi. However, pi does not equal 3. Pi is approximately 3.14. If we plug in 3.14 for pi, we find that Quantity A is greater.

In the video, I say that we can SOMETIMES get away with plugging in 3 for pi. HOWEVER, these are typically cases with multiple choice questions in which the answer choices are sufficiently spread apart enough to allow for us to use 3 an an approximation for pi.

Thanks Brent....I appreciate

Sir the second question from the bottom (Related sources)...
How did we knew the center of the circle is at coordinates (-6,-7)? In the question it only states that the center has coordinates and then full stop. Its really confusing.
greenlight-admin's picture

You're referring to http://greprepclub.com/forum/in-the-xy-plane-the-point-with-coordinates-...

I made a query about the post, and I see that the question has now been corrected.

Thanks a lot Sir :)

http://greprepclub.com/forum/ab-is-a-diameter-of-the-circle-above-1832.html

"Avg length of any 2 or more chords will always be less than diameter" Is it true?
greenlight-admin's picture

Question link: http://greprepclub.com/forum/ab-is-a-diameter-of-the-circle-above-1832.html

Yes it's true..as long as the chords are NOT the diameters. The statement is true since the diameter is the longest possible chord in a circle.

http://greprepclub.com/forum/in-the-gure-above-o-and-p-are-the-centers-of-the-two-circl-1856.html

Why the shaded figure, cant be the rhombus? two equilateral triangle if we keep them in opposite joining at their bases, can it be the rhombus?
greenlight-admin's picture

Question link: http://greprepclub.com/forum/in-the-gure-above-o-and-p-are-the-centers-o...

Yes, the shaded figure is definitely a rhombus. I just divided that rhombus into two equal equilateral triangles so I could apply the special area formula.

in case of rhombus area will be (diagonal1 * diagonal2) / 2.

rhombus have the property that, if one diagonal is r then other
will be sqrt(3) * r.

(sqrt(3) r * r) / 2
( sqrt(3) r^2 ) / 2 => B is the answer.

https://greprepclub.com/forum/the-circle-above-has-area-10917.html

One of the assumptions of geometry was to avoid visual estimation. There is no doubt that the diameter is 10 but how can we say for sure that AB is not the diameter of the circle? AB can be a cord as well with a value lower than 10. Can you please explain
greenlight-admin's picture

Question link: https://greprepclub.com/forum/the-circle-above-has-area-10917.html

Be careful. A circle with area 25 does NOT have a diameter of 10 units.

IF it were the case that the area were 25π, then the diameter would be 10. However, since the area is 25, the diameter is must less than 10.

Does that help?

Cheers,
Brent

Yes that helps. I'm making too many silly calculation errors.

https://greprepclub.com/forum/in-the-gure-above-o-and-p-are-the-centers-of-the-two-circl-1856.html
How did you know it was an equilaterial triangle. It could have been any type of triangle too
greenlight-admin's picture

I created a post to specifically answer your question: https://greprepclub.com/forum/in-the-gure-above-o-and-p-are-the-centers-...

Cheers,
Brent

https://greprepclub.com/forum/in-the-above-figure-which-one-of-the-following-could-12143.html
I thought in could be questions we only need to find one instance where it's true? If B equals 90,then (B-a/2) can give an angle greater than zero
greenlight-admin's picture

Question link: https://greprepclub.com/forum/in-the-above-figure-which-one-of-the-follo...

IMPORTANT: All FIVE angles in the diagram must be greater than zero.

So, if it's possible that b = 90, then we must ensure that ALL 5 angles are positive.

If b = 90 and a = 72, then (b - a/2) is positive number (GOOD)
If b = 90 and a = 72, then (2a - b) is positive number (GOOD)
If b = 90 and a = 72, then (2a - 2b) is NOT a positive number
So, b cannot equal 90

Does that help?

Cheers,
Brent

Understood perfectly. I keep forgetting about the not draw to scale disclaimer. For example this question https://greprepclub.com/forum/in-the-semicircle-above-the-length-of-arc-ac-is-equal-to-t-5616.html we were told it's a semi circle but u made it a full circle. you also made an assumption that the length of arc AB=BD even when the question tells us it's less. Does this mean that in geometric figures we can make assumptions we like
greenlight-admin's picture

Question link: https://greprepclub.com/forum/in-the-semicircle-above-the-length-of-arc-...

I didn't assume that arc AB = arc BD.
Instead, I examined what WOULD happen IF it were the case that arc AB = arc BD.
Once I was able to identify would happen IF arc AB = arc BD, then I was able to extrapolate what happens when arc AB < arc BD.

Keep in mind that this is a super tricky question.
As is often the case with difficult questions, the solution requires some outside-the-box thinking.

Cheers,
Brent

Why isn't it a solution then
greenlight-admin's picture

Hi Stunnerxoxo,

When you post a response to an ongoing thread, please use the reply button so I (and others reading this) know which question you're referring to.

I believe you're asking about my response that begins with "IMPORTANT: All FIVE angles in the diagram must be greater than zero."

The five angles in the diagram are: b - a/2, a/2 + 2b, 2a -2b, 2a - b, and a

ALL FIVE angles must have positive measurements.
If b = 90 and a = 72, then 4 of the five angles are positive.

However, when we have a problem with the angle represented by (2a - 2b)
If b = 90 and a = 72, then 2a - 2b = 2(72) - 2(90) = 144 - 180 = -36
So, one of the angles in the diagram is -36 degrees.

Since this makes no sense, we can conclude that angle b CANNOT be 90 degrees.

Cheers,
Brent

Great thanks

Hello Sir,

For this question can I also conclude that diameter is the longest line inside the circle hence the side of the triangle is always small.

https://greprepclub.com/forum/gre-math-challenge-134-the-vertices-of-an-equilateral-792.html
greenlight-admin's picture

Question link: https://greprepclub.com/forum/gre-math-challenge-134-the-vertices-of-an-...

That's a perfectly sound (and clever!) solution. Nice work!!

https://greprepclub.com/forum/the-area-of-a-circular-region-with-diameter-x-14560.html
In this question has the question mentioned that the square is inscribed in a circle?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/the-area-of-a-circular-region-with-diamete...

Great question!

No, the question doesn't specify a square is inscribed in a circle.
However, the question tells us that x is the circle's diameter, AND x is also the square's diagonal.
So, we can significantly shorten our solution time by recognizing that we can actually sketch both shapes in a single diagram.

Does that help?

Cheers,
Brent

Yes It is quite informative.

https://greprepclub.com/forum/the-area-of-a-circular-region-with-diameter-x-14560.html

I solved this question by finding the area of the circle for quantity A and the area of the square for quantity B. In case of finding the area of the square, I assumed that the 4 triangles formed by the sides and diagonals of the square have equal area and each of these triangles are 45-45-90 triangles since diagonals of a square are perpendicular bisectors of each other. Are these assumptions correct?
greenlight-admin's picture

Link: https://greprepclub.com/forum/the-area-of-a-circular-region-with-diamete...

That's correct. If you cut a square into 4 triangles (like they do with a square sandwich), each triangle will be a 45-45-90 triangle.

For example: http://2.bp.blogspot.com/-JF4_XJwFOE4/T-MNb9QeVGI/AAAAAAAAAPI/Ms43TwwSrY...

https://greprepclub.com/forum/the-circle-has-center-0-and-rt-13949.html

The Diameter is the longest chord in a circle and it looks like there can there be another chord with the same length that's not the diameter?
greenlight-admin's picture

Question link: https://greprepclub.com/forum/the-circle-has-center-0-and-rt-13949.html

If a line passes through the center of a circle, then that line must be the diameter of the circle.
So, if there's a chord that's the same length as the diameter, then that chord must also be a diameter.

https://greprepclub.com/forum/circle-a-has-area-a-semicircle-b-has-area-a-2316.html
Please solve it Brent..
greenlight-admin's picture

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