170+ CAT Geometry Questions With Video Solutions And PDF
Geometry is an important and challenging topic in the CAT exam with a lot of weightage. CAT Geometry questions are asked from topics including Triangles, Circles, Quadrilaterals, Polygons and so on. To perform Geometry, one must thoroughly understand concepts, and formulas and gain problem-solving skills. Previous years' question papers are invaluable resources for CAT preparation, especially for mastering the CAT Quantitative Aptitude section. By solving the questions from CAT's previous papers, candidates can understand the types of questions asked, the level of difficulty, and the exam pattern. Below, you can find all those Geometry questions separated year-wise, along with the video solution for each question. Keep practising free CAT mocks where you'll get a fair idea of how questions are asked, and type of questions asked of CAT Geometry Questions. Also, you can download all the below questions in a PDF format consisting of video solutions for every problem explained by the CAT experts. Click the link below to download the CAT Geometry Questions with video Solutions PDF.
CAT Geometry Topic-wise Weightage Over Past 6 Years
Topic | 2023 | 2022 | 2021 | 2020 | 2019 | 2018 |
Triangles | 3 | 4 | 2 | 2 | 2 | 3 |
Circles | 1 | 1 | 1 | 3 | 3 | 4 |
Quadrilaterals | 1 | 3 | 5 | 0 | 0 | 5 |
Polygons | 1 | 1 | 2 | 2 | 2 | 0 |
| Mensuration | 2 | 0 | 0 | 3 | 3 | 1 |
| Co-ordinate Geometry | 1 | 0 | 0 | 1 | 1 | 0 |
| Total | 9 | 9 | 10 | 11 | 11 | 13 |
CAT Geometry Formulas PDF
CAT Geometry is one of the most important topics in the quantitative aptitude section, and it is vital to have a clear understanding of the formulas related to them. As mentioned earlier, there will be high weightage for this concept if you can compare the past few CAT question papers. To help the aspirants to ace this topic, we have made a PDF containing a comprehensive list of formulas, tips, and tricks that you can use to solve Geometry questions with ease and speed. Click on the below link to download the CAT Geometry formulas PDF.
1. Tangents on a circle
Tangents:
Direct common tangent: $$PQ^2=RS^2=D^2-\left(r_1-r_2\right)^2$$, where D is the distance between the centres:
Transverse common tangent: $$PQ^2=RS^2=D^2-\left(r_1+r_2\right)^2$$, where D is the distance between the centres:
2. Area, inradius, circumradius of triangles
If x is the side of an equilateral triangle then the
Altitude (h) =$$\frac{\sqrt{\ 3}}{2}x$$
Area =$$\frac{\sqrt{\ 3}}{4}x^2$$
Inradius = $$\frac{1}{3}\times\ h$$
Circumradius = $$\frac{2}{3}\times\ h$$
▪ Area of an isosceles triangle =$$\frac{a}{4}\sqrt{\ 4c^2-a^2}$$ (where a, b and c are the length of the sides of BC, AC and AB respectivelyand b = c)
Special triangles :
30^{0}, 60^{0} and 90^{0}
45^{0}, 45^{0} and 90^{0}
CAT 2024 Geometry questions
Question 1
The coordinates of the three vertices of a triangle are: (1, 2), (7, 2), and (1, 10). Then the radius of the incircle of the triangle is
correct answer:-2
Question 2
A circular plot of land is divided into two regions by a chord of length $$10\sqrt{3}$$ meters such that the chord subtends an angle of 120° at the center. Then, the area, in square meters, of the smaller region is
correct answer:-4
Question 3
Three circles of equal radii touch (but not cross) each other externally. Two other circles, X and Y, are drawn such that both touch (but not cross) each of the three previous circles. If the radius of X is more than that of Y, the ratio of the radii of X and Y is
correct answer:-1
Question 4
ABCD is a trapezium in which AB is parallel to CD. The sides AD and BC when extended, intersect at point E. If AB = 2 cm, CD = 1 cm, and perimeter of ABCD is 6 cm, then the perimeter, in cm, of $$\triangle AEB$$ is
correct answer:-1
Question 5
ABCD is a rectangle with sides AB = 56 cm and BC = 45 cm, and E is the midpoint of side CD. Then, the length, in cm, of radius of incircle of $$\triangle ADE$$ is
correct answer:-10
Question 6
A regular octagon ABCDEFGH has sides of length 6 cm each. Then the area, in sq. cm, of the square ACEG is
correct answer:-4
Question 7
The midpoints of sides AB, BC, and AC in ΔABC are M, N, and P, respectively. The medians drawn from A, B, and C intersect the line segments MP, MN and NP at X, Y, and Z, respectively. If the area of ΔABC is 1440 sq cm, then the area, in sq cm, of $$\triangle XYZ$$ is
correct answer:-90
Question 8
The surface area of a closed rectangular box, which is inscribed in a sphere, is 846 sq cm, and the sum of the lengths of all its edges is 144 cm. The volume, in cubic cm, of the sphere is
correct answer:-3
CAT 2023 Geometry questions
Question 1
A triangle is drawn with its vertices on the circle C such that one of its sides is a diameter of C and the other two sides have their lengths in the ratio a : b. If the radius of the circle is r, then the area of the triangle is
correct answer:-2
Question 2
Let C be the circle $$x^{2} + y^{2} + 4x - 6y - 3 = 0$$ and L be the locus of the point of intersection of a pair of tangents to C with the angle between the two tangents equal to $$60^{\circ}$$. Then, the point at which L touches the line $$x$$ = 6 is
correct answer:-2
Question 3
Let $$\triangle ABC$$ be an isosceles triangle such that AB and AC are of equal length. AD is the altitude from A on BC and BE is the altitude from B on AC. If AD and BE intersect at O such that $$\angle AOB = 105^\circ$$, then $$\frac{AD}{BE}$$ equals
correct answer:-3
Question 4
A quadrilateral ABCD is inscribed in a circle such that AB : CD = 2 : 1 and BC : AD = 5 : 4. If AC and BD intersect at the point E, then AE : CE equals
correct answer:-3
Question 5
A rectangle with the largest possible area is drawn inside a semicircle of radius 2 cm. Then, the ratio of the lengths of the largest to the smallest side of this rectangle is
correct answer:-1
Question 6
In a rectangle ABCD, AB = 9 cm and BC = 6 cm. P and Q are two points on BC such that the areas of the figures ABP, APQ, and AQCD are in geometric progression. If the area of the figure AQCD is four times the area of triangle ABP, then BP : PQ : QC is
correct answer:-3
Question 7
In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is
correct answer:-54
Question 8
In a right-angled triangle ∆ABC, the altitude AB is 5 cm, and the base BC is 12 cm. P and Q are two points on BC such that the areas of $$\triangle ABP, \triangle ABQ$$ and $$\triangle ABC$$ are in arithmetic progression. If the area of ∆ABC is 1.5 times the area of $$\triangle ABP$$, the length of PQ, in cm, is
correct answer:-2
CAT 2022 Geometry questions
Question 1
In triangle ABC, altitudes AD and BE are drawn to the corresponding bases. If $$\angle BAC = 45^{\circ}$$ and $$\angle ABC=\theta\ $$, then $$\frac{AD}{BE}$$ equals
correct answer:-4
Question 2
Suppose the medians BD and CE of a triangle ABC intersect at a point O. If area of triangle ABC is 108 sq. cm., then, the area of the triangle EOD, in sq. cm., is
correct answer:-9
Question 3
A trapezium $$ABCD$$ has side $$AD$$ parallel to $$BC, \angle BAD = 90^\circ, BC = 3$$ cm and $$AD= 8$$ cm. If the perimeter of this trapezium is 36 cm, then its area, in sq. cm, is
correct answer:-66
Question 4
Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals
correct answer:-10
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Frequently Asked Questions
Video solutions can be a helpful resource for candidates preparing for CAT geometry questions. They can provide a step-by-step explanation of how to solve the problem, helping candidates better understand the concept and formula.
Triangles, Circles, Quadrilaterals, Polygons, 3-D Geometry and Coordinate Geometry are the most important topics that candidates should have well understanding. They should practice a wide range of questions related to each topic to excel in the Geometry topic in the CAT quant section.
