CAT 2019 Question Paper | Quants Slot 1

CAT Questions

CAT previous year papers are known to have questions that layer 2 or 3 concepts from different topics. This question fits into that bucket where it uses multiple concepts including Co-ordinate geometry, Circles & Triangles. It is a tricky problem that may end up as a time guzzler. Hence it is important to attempt these questions only if you have focussed on geometry as part of your CAT online preparation.

Question 8 : Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is [TITA]

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Video Explanation

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Explanatory Answer

We know that the equation of the straight line is 3x + 5y = 45

The intercepts are (15,0) and (0,9) respectively
Since it's a right-angled triangle, we know that Circumradius (R) =
Circumradius = =
We know that is approximately equal to 6
So, from trial and error to find the closest number, we find that the value of Circumradius is very close to 9
So, the integer closest to L = 9

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The question is "Let T be the triangle formed by the straight line 3x + 5y - 45 = 0 and the coordinate axes. Let the circumcircle of T have radius of length L, measured in the same unit as the coordinate axes. Then, the integer closest to L is [TITA] "

Hence, the answer is 9