Question: Intersecting Circles

Comment on Intersecting Circles

Thanks you so much for the videos. I just completed watching all videos of geometry. This is a great help for me. I have learned a lot. Hope this will help me for my gmat preparation.

This is blowing my mind

alternatively to the formula: drop an altitude, which results in two 90:60:30 triangles. From there base will be half the hypotenuse = 6/2=3 and therefore hight will be 3*root3

then are as usual: (b*h)/2 --> (6*3*root3)/2
gmat-admin's picture

That works too!

if you start of with this can you solve the problem by eliminating all solutions that don't include -18root3? or would it be a wild guess?
gmat-admin's picture

Great idea!

We know that the area of ONE equilateral triangle is 9√3
So, once you're certain how many equilateral triangle areas you need to subtract (in this case, we must subtract 2 of those areas), then you can start eliminating.


Does this qs also deserve a 700-800 category listing? Mind blowing...
gmat-admin's picture

Yes, this is definitely a 700+ level question. VERY tricky!

Aside: if you hover your cursor over each colored square next to the PLAY button, you'll see the difficulty level of each question.

Green: 350 - 500
Yellow: 510 - 650
Red: 660 - 800


Hi Brent! Is there a link to download the Geometry slides for offline review? Thanks!
gmat-admin's picture

If you go here (, you'll find a downloadable pdf of all GMAT math flashcards. They contain more than just Geometry, but I think they're useful.

man!! i am in love with your videos
gmat-admin's picture

Thanks for that!

Hi Brent, I solved this question with the following approach:

Let the two intersecting points be AB. Draw AB and OP. Let them intersect at X. Area of sector OAB is 12pi. Area of triangle OAB is 9*root(3)

Since the area that we have to find is twice of 12pi - 9*root(3), answer is 24pi - 18root(3)
gmat-admin's picture

Nice work!!

Question: DO we have to remember the formula of a sphere's volume
gmat-admin's picture

No, you don't need to memorize the formula for the volume of a sphere.
If the GMAT were to create a question involving a sphere's volume, they will undoubtedly provide the necessary formula.
Here's an example of such a question:

Another great video Brent and mind blowing. To clarify, when we calculate a+b area, is this belong to circle C or P or both? Same with rest b+c areas...etc. Thanks Brent
gmat-admin's picture

All parts inside the blue (and the later yellow) area belong to BOTH circles .

Thanks Brent for confirmation. Now I'm clear that for common area calculation of both circle is same as circumference area calculation except to deduct the duplicate b,d part.

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