Lesson: Circles

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

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.

You're referring to http://gre.myprepclub.com/forum/in-the-xy-plane-the-point-with-coordinat...

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

Question link: http://gre.myprepclub.com/forum/ab-is-a-diameter-of-the-circle-above-183...

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.

Question link: http://gre.myprepclub.com/forum/in-the-gure-above-o-and-p-are-the-center...

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.

Question link: https://gre.myprepclub.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

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

Cheers,
Brent

Question link: https://gre.myprepclub.com/forum/in-the-above-figure-which-one-of-the-fo...

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

Question link: https://gre.myprepclub.com/forum/in-the-semicircle-above-the-length-of-a...

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

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

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

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

Question link: https://gre.myprepclub.com/forum/the-area-of-a-circular-region-with-diam...

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

Link: https://gre.myprepclub.com/forum/the-area-of-a-circular-region-with-diam...

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...

Question link: https://gre.myprepclub.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.

Here's my full solution: https://gre.myprepclub.com/forum/circle-a-has-area-a-semicircle-b-has-ar...

Cheers,
Brent

Question link: https://gmatclub.com/forum/a-certain-recipe-makes-enough-batter-for-exac...

This question requires us to recognize that a 10-inch pancake requires more batter than a 5-inch pancake.
In other words, a 10-inch pancake has a greater volume than a 5-inch pancake.
Pancakes are in the shape of cylinders.
The volume of a cylinder = πr²h = (πr²)(h) = (area of the cylinder's base)(h)
Since the two pancakes have the same thickness (i.e., the same height), it's the areas of the two pancakes' bases that account for the difference in batter requirements.

That's a real nice short/elegant solution!
Great thinking, Ravin!