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Sounds like a good plan. Obviously there's a lot more on the GMAT than what I cover in my RUclips videos, so you might consider one of our comprehensive courses: www.dominatethegmat.com/video-purchase/. Since you're going through the OG, I would recommend the Gold or Platinum packages so that you get my video solutions for all of the questions in the Official Guide. I think they'll really help you apply the ideal approach for each question!
I am enjoying the videos and find them very educational. Perhaps it should be obvious somehow, but is there some part of the question that indicates the triangle goes to the edges of the circle? All the question states is that the triangle has 3 equal sides. Does the word 'inscribed' mean that those equal sides would be long enough to reach the edge of the circle? When I first read it I thought it would be impossible to tell how big the triangle in the question was. Thanks for all your videos and help.
Yes, that's right, it's the word "inscribed" that tells you the triangle is big enough to touch the circle at the vertices. The key is that it touches perfectly, so that it doesn't come up short and doesn't extend beyond the circumference of the circle. That same understanding applies to any geometric figure "inscribed" inside another figure (e.g. for a circle inscribed in a square, the circle must be big enough to touch the sides of the square in exactly four points, with the sides of the square being the same length as the circle's diameter). Glad you're enjoying the videos! And I hope you'll consider one of my full courses whenever you're ready to dive deeper. In the meantime, let me know how else I can help.
An easier way to go about this is to recognize that the radius of a circle circumscribing an equilateral triangle is equal to the side of the equilateral triangle divided by the square root of 3. With this thinking in mind, the question can be solved in less than 1 minute.
The question stem tells us that the triangle has "three equal sides." By definition that means it's an equilateral triangle where each of the angles has the same degree measure as well. Since the angles in a triangle sum to 180 degrees, each angle in an equilateral triangle = 180/3 = 60 degrees.
How can you assume radius of circle to be 2? To be honest, i dont want to learn thru guesswork. Conceptual understanding always works (unless the truth here is that conceptual answers cannot be derived in this question)
He is saying you can use any number for the radius, if you used 4 or 12 or 24 you would always be able to factor the answer back down to the correct answer shown.
The best way is to memorize the common 30-60-90 right triangle template, which I cover in detail in my course. You could also use the Pythagorean Theorem.
Its funny that most people know the formula to find the area of a triangle, but don't actually think about the meaning of the word area. #Basic princples
The area of equilateral triangle can be used directly after you know that the side is √3 but the problem arises with radius ...what to choose an even radius or odd becz. Odd radius gives different answer
If you choose a different radius, for example an odd number for "r," you're correct that you'll end up with a different area for the triangle. But you'll also end up with a different area for the circle, and the ratio of the triangle area to the circle area will be the same. Thus you still end up getting the same answer.
@@dominatethegmat There is a rule governing an equilateral triangle inscribed in a circle which states that the radius of the circle is equal to the side of the equilateral triangle divided by the square root of 3. You simply need to choose a variable for the side of the triangle and use this to estimate the areas of the circle and triangle. The variable will cancel out and you will arrive at answer choice C. This takes less than a minute. Also note that the area of an equilateral triangle can be gotten by multiplying the square of the side by square root 3 and dividing by 4.
@@hyceinthkum3693 Yep, that's a great shortcut. You can obviously figure that out by making up numbers and applying the rules of a 30-60-90 right triangle, but it all boils down to radius = (equilateral triangle side) / root3 as you explained. Thanks for sharing!
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the height is much easier calculated by adding up the 1 from the triangle right lower corner and 2 from the radius, from middle going up.
Why choose 2 as the radius, and which other numbers can and can't be used.
Love your videos sir... I have just a month to prepare for GMAT.. just following the og and preparing from your videos.. thank u so much ...
Sounds like a good plan. Obviously there's a lot more on the GMAT than what I cover in my RUclips videos, so you might consider one of our comprehensive courses: www.dominatethegmat.com/video-purchase/. Since you're going through the OG, I would recommend the Gold or Platinum packages so that you get my video solutions for all of the questions in the Official Guide. I think they'll really help you apply the ideal approach for each question!
Good question. Yes, the long side (height) of a 30-60-90 right triangle is root3 times as large as the short side.
I am enjoying the videos and find them very educational.
Perhaps it should be obvious somehow, but is there some part of the question that indicates the triangle goes to the edges of the circle? All the question states is that the triangle has 3 equal sides. Does the word 'inscribed' mean that those equal sides would be long enough to reach the edge of the circle? When I first read it I thought it would be impossible to tell how big the triangle in the question was.
Thanks for all your videos and help.
Yes, that's right, it's the word "inscribed" that tells you the triangle is big enough to touch the circle at the vertices. The key is that it touches perfectly, so that it doesn't come up short and doesn't extend beyond the circumference of the circle. That same understanding applies to any geometric figure "inscribed" inside another figure (e.g. for a circle inscribed in a square, the circle must be big enough to touch the sides of the square in exactly four points, with the sides of the square being the same length as the circle's diameter). Glad you're enjoying the videos! And I hope you'll consider one of my full courses whenever you're ready to dive deeper. In the meantime, let me know how else I can help.
Thank You!
My pleasure!
use the formula of area of equilateral triangle root3/4 * a sqaure
will be shorter
An easier way to go about this is to recognize that the radius of a circle circumscribing an equilateral triangle is equal to the side of the equilateral triangle divided by the square root of 3. With this thinking in mind, the question can be solved in less than 1 minute.
Nice shortcut. Thanks for sharing!
Thank you, Brett!
My pleasure!
How do you get 60 degree angles in the triangle?
The question stem tells us that the triangle has "three equal sides." By definition that means it's an equilateral triangle where each of the angles has the same degree measure as well. Since the angles in a triangle sum to 180 degrees, each angle in an equilateral triangle = 180/3 = 60 degrees.
If you use an odd number radius you get answer choice E, I tested r = 1 and r = 3 and got E but for even r you get C...
I tested with r=3 and used area of equilateral triangle, the answer was C.
Where’s 1/2bh came from ?
That's the formula for the area of a triangle. It's one of the formulas you should know/memorize for the GMAT.
How can you assume radius of circle to be 2? To be honest, i dont want to learn thru guesswork. Conceptual understanding always works (unless the truth here is that conceptual answers cannot be derived in this question)
He is saying you can use any number for the radius, if you used 4 or 12 or 24 you would always be able to factor the answer back down to the correct answer shown.
What is gmat ??
The GMAT is a standardized test that is used by many business schools around the world as part of their application process for admission.
How we get that radical 3?? Next time please explain every single number appear..
The best way is to memorize the common 30-60-90 right triangle template, which I cover in detail in my course. You could also use the Pythagorean Theorem.
Sir is it 650+ level question?
I am not great at quant, but I found it easy to solve. Thank you for posting...
You're better than you think you are! Yes, this is considered a challenging geometry question.
Dominate the GMAT thanks for a positive reply....
Easier way is to use the sen rule when you divide the triangule
Its funny that most people know the formula to find the area of a triangle, but don't actually think about the meaning of the word area. #Basic princples
The area of equilateral triangle can be used directly after you know that the side is √3 but the problem arises with radius ...what to choose an even radius or odd becz. Odd radius gives different answer
If you choose a different radius, for example an odd number for "r," you're correct that you'll end up with a different area for the triangle. But you'll also end up with a different area for the circle, and the ratio of the triangle area to the circle area will be the same. Thus you still end up getting the same answer.
@@dominatethegmat There is a rule governing an equilateral triangle inscribed in a circle which states that the radius of the circle is equal to the side of the equilateral triangle divided by the square root of 3. You simply need to choose a variable for the side of the triangle and use this to estimate the areas of the circle and triangle. The variable will cancel out and you will arrive at answer choice C. This takes less than a minute. Also note that the area of an equilateral triangle can be gotten by multiplying the square of the side by square root 3 and dividing by 4.
@@hyceinthkum3693 Yep, that's a great shortcut. You can obviously figure that out by making up numbers and applying the rules of a 30-60-90 right triangle, but it all boils down to radius = (equilateral triangle side) / root3 as you explained. Thanks for sharing!