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Geometry CAT Previous Year Questions with Answer PDF

Question for CAT Previous Year Questions: Geometry
Try yourself:Let C be the circle x2 + y2 + 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°. Then, the point at which L touches the line x = 6 is

[2023]

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Question for CAT Previous Year Questions: Geometry
Try yourself: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

[2023]

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Question for CAT Previous Year Questions: Geometry
Try yourself: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 ΔABP, ΔABQ and ΔABC are in arithmetic progression. If the area of ΔABC is 1.5 times the area of ΔABP, the length of PQ, in cm, is

[2023]

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Question for CAT Previous Year Questions: Geometry
Try yourself: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

[2023]

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Question for CAT Previous Year Questions: Geometry
Try yourself: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

[2023]

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Question for CAT Previous Year Questions: Geometry
Try yourself:All the vertices of a rectangle lie on a circle of radius R . If the perimeter of the rectangle is P , then the area of the rectangle is

[2022]

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Question for CAT Previous Year Questions: Geometry
Try yourself:A circle of diameter 8 inches is inscribed in a triangle ABC where∠ABC=90. If BC = 10 inches then the area of the triangle in square inches is

[2021]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Suppose the length of each side of a regular hexagon ABCDEF is 2 cm.It T is the mid point of CD,then the length of AT, in cm, is

[2021]

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Question for CAT Previous Year Questions: Geometry
Try yourself:If the area of a regular hexagon is equal to the area of an equilateral triangle of side 12 cm, then the length, in cm, of each side of the hexagon is

[2021]

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Question for CAT Previous Year Questions: Geometry
Try yourself:AB is a diameter of a circle of radius 5 cm. Let P and Q be two points on the circle so that the length of PB is 6 cm, and the length of AP is twice that of AQ. Then the length, in cm, of QB is nearest to

[2019]

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Question for CAT Previous Year Questions: Geometry
Try yourself:In a triangle ABC, medians AD and BE are perpendicular to each other, and have lengths 12 cm and 9 cm, respectively. Then, the area of triangle ABC, in sq cm, is

[2019]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is

[2019]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Let A and B be two regular polygons having a and b sides, respectively. If b = 2a and each interior angle of B is 3 / 2 times each interior angle of A, then each interior angle, in degrees, of a regular polygon with a + b sides is

[2019 TITA]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is

[2019]

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Question for CAT Previous Year Questions: Geometry
Try yourself:In a circle with centre O and radius 1 cm, an arc AB makes an angle 60 degrees at O. Let R be the region bounded by the radii OA, OB and the arc AB. If C and D are two points on OA and OB, respectively, such that OC = OD and the area of triangle OCD is half that of R, then the length of OC, in cm, is

[2018]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Given an equilateral triangle T1 with side 24 cm, a second triangle T2 is formed by joining the midpoints of the sides of T1. Then a third triangle T3 is formed by joining the midpoints of the sides of T2. If this process of forming triangles is continued, the sum of the areas, in sq cm, of infinitely many such triangles T1, T2, T3,... will be

[2018]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Let ABCD be a rectangle inscribed in a circle of radius 13 cm. Which one of the following pairs can represent, in cm, the possible length and breadth of ABCD?

[2018]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Points E, F, G, H lie on the sides AB, BC, CD, and DA, respectively, of a square ABCD. If EFGH is also a square whose area is 62.5% of that of ABCD and CG is longer than EB, then the ratio of length of EB to that of CG is:

[2018]

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Question for CAT Previous Year Questions: Geometry
Try yourself:In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is

[2018]

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Question for CAT Previous Year Questions: Geometry
Try yourself:On a triangle ABC, a circle with diameter BC is drawn, intersecting AB and AC at points P and Q, respectively. If the lengths of AB, AC, and CP are 30 cm, 25 cm, and 20 cm respectively, then the length of BQ, in cm, is

[2018 TITA]

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Question for CAT Previous Year Questions: Geometry
Try yourself:A chord of length 5 cm subtends an angle of 60° at the centre of a circle. The length, in cm, of a chord that subtends an angle of 120° at the centre of the same circle is

[2018]

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Question for CAT Previous Year Questions: Geometry
Try yourself:From a triangle ABC with sides of lengths 40 ft, 25 ft and 35 ft, a triangular portion GBC is cut off where G is the centroid of ABC. The area, in sq ft, of the remaining portion of triangle ABC is:

[2017]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Let ABC be a right-angled triangle with BC as the hypotenuse. Lengths of AB and AC are 15 km and 20 km, respectively. The minimum possible time, in minutes, required to reach the hypotenuse from A at a speed of 30 km per hour is:

[2017 TITA]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

[2017]

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Question for CAT Previous Year Questions: Geometry
Try yourself:The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

[2017]

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Question for CAT Previous Year Questions: Geometry
Try yourself:ABCD is a quadrilateral inscribed in a circle with centre O. If ∠COD = 120 degrees and ∠BAC = 30 degrees, then the value of ∠BCD (in degrees) is

[2017 TITA]

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Question for CAT Previous Year Questions: Geometry
Try yourself:If three sides of a rectangular park have a total length 400 ft., then the area of the park is maximum when the length (in ft.) of its longer side is

[2017 TITA]

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Question for CAT Previous Year Questions: Geometry
Try yourself:Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB, BC, and CA is 4(√2 - 1) cm, then the area, in sq. cm, of the triangle ABC is

[2017 TITA]

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The document Geometry CAT Previous Year Questions with Answer PDF is a part of the CAT Course Quantitative Aptitude (Quant).
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FAQs on Geometry CAT Previous Year Questions with Answer PDF

1. What are the basic principles of geometry?
Ans. Geometry is based on fundamental principles such as points, lines, planes, angles, and shapes. These elements form the basis for all geometric concepts and calculations.
2. How is geometry used in real life?
Ans. Geometry is used in various real-life applications such as architecture, engineering, design, and navigation. It helps in creating structures, solving spatial problems, and understanding the relationships between shapes and objects.
3. What is the importance of geometry in mathematics?
Ans. Geometry plays a crucial role in mathematics as it helps in developing spatial reasoning, problem-solving skills, and logical thinking. It provides a foundation for understanding complex mathematical concepts and theories.
4. What are the different types of angles in geometry?
Ans. In geometry, angles are classified into different types based on their measures. Some common types of angles include acute angles (less than 90 degrees), obtuse angles (greater than 90 degrees), right angles (exactly 90 degrees), and straight angles (exactly 180 degrees).
5. How can I improve my geometry skills?
Ans. To improve your geometry skills, practice solving geometric problems regularly, use visualization techniques to understand spatial relationships, and study the properties of different shapes and angles. Additionally, seeking help from a tutor or using online resources can also be beneficial in enhancing your geometry skills.
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