Geometry question

Question

What is the value of x in the attached figure where the line on the circles' base is tangent to both the circles with radius 2 and 1?

Rich.C@EMPOWERgmat.com · Answer

Hi ricky01,

When posting GMAT questions, it's important to post the entire prompt (including the 5 answer choices and the correct answer). Sometimes the answers provide a clue as to how you can go about solving the problem.

Have you posted all of the necessary information from this question? Are these two circles tangent to one another and are we meant to assume that the line connects the two centers of those circles? Assuming those two details are implied, then the length of that line would be the sum of the two radii. If the two circles are not tangent, then we would need some additional information to determine the distance between those two circles on that line.

GMAT assassins aren't born, they're made,
Rich

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ricky01 · Answer

Rich.C@EMPOWERgmat.com wrote:Hi ricky01, When posting GMAT questions, it's important to post the entire prompt (including the 5 answer choices and the correct answer). Sometimes the answers provide a clue as to how you can go about solving the problem. Have you posted all of the necessary information from this question? Are these two circles tangent to one another and are we meant to assume that the line connects the two centers of those circles? Assuming those two details are implied, then the length of that line would be the sum of the two radii. If the two circles are not tangent, then we would need some additional information to determine the distance between those two circles on that line. GMAT assassins aren't born, they're made, Rich Hi Rich, Thanks for your help. I'm afraid I don't remember where I saw this question but I kind of just remembered it and needed help. Also the line that the circles are on is tangent to the circles, don't think the circles are tangent to each other. And yes, the line connects the radii of the 2 circles. What would the answer be then please? Also why would the length of that line be the sum of the two radii if the circles were tangent to each other? Thanks so much!

OptimusPrep · Answer

ricky01 wrote:What is the value of x in the attached figure where the line on the circles' base is tangent to both the circles with radius 2 and 1?

In the triangle, Base = 3, Height = 1
Hence the hypotenuse = x = (3^2 + 1^2) = √10

regor60 · Answer

OptimusPrep wrote:ricky01 wrote:What is the value of x in the attached figure where the line on the circles' base is tangent to both the circles with radius 2 and 1? In the triangle, Base = 3, Height = 1 Hence the hypotenuse = x = (3^2 + 1^2) = √10 How has it been established that the base of the large circle is 2 ? That is only the case if it's a radius, which it is not according to the drawing. The question is insufficiently specified

Matt@VeritasPrep · Answer

Is the problem asking for the length of the line to which each of the circles is tangent? In that case, we'd have something like this:

Matt@VeritasPrep · Answer

Whoops, just to finish that last one, we'd then have x² + 1² = (1 + 2)² or x² + 1 = 9 x² = 8 x = 2√2

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