Geometry - Level 2 (PYQs)
- IIMwalaBanda
- Aug 10
- 3 min read
1. [CAT 2021, Slot 1] A circle of diameter 8 inches is inscribed in a triangle ABC where angle ABC = 90°. If BC = 10 inches, find the area of the triangle (in square inches). (P)
(a) 100
(b) 110
(c) 120
(d) 130
2. [CAT 2023, Slot 1] 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 triangles ABP, ABQ, and ABC are in arithmetic progression. If the area of triangle ABC is 1.5 times the area of triangle ABP, find the length of PQ (in cm). (P)
(a) 1
(b) 1.5
(c) 2
(d) 2.5
3. [CAT 2024, Slot 1] In a right triangle ADE, the two legs measure 28 cm and 45 cm. Find the inradius of this triangle (in cm). (P)
(a) 8
(b) 9
(c) 10
(d) 12
4. [CAT 2024, Slot 2] A triangle has sides of length 10 cm, 6 cm, and 8 cm. Find its inradius (in cm). (P)
(a) 1.5
(b) 2
(c) 2.5
(d) 3
5. [CAT 2022, Slot 2] Regular polygons A and B have their number of sides in the ratio 1:2, and their interior angles in the ratio 3:4. Find the number of sides of polygon B. (P)
(a) 8
(b) 9
(c) 10
(d) 12
6. [CAT 2024, Slot 2] 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 the perimeter of ABCD is 6 cm, find the perimeter, in cm, of triangle AEB. (P)
(a) 6
(b) 7
(c) 8
(d) 9
7. [CAT 2021, Slot 2] ABCD is a trapezium, and P is the midpoint of CD such that ABPD is a parallelogram. If the difference between the areas of parallelogram ABPD and triangle BPC is 10 sq cm, find the area, in sq cm, of trapezium ABCD. (P)
(a) 24
(b) 27
(c) 30
(d) 33
8. [CAT 2023, Slot 1] 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 point E, find AE:CE. (P)
(a) 8:5
(b) 5:8
(c) 2:1
(d) 4:5
9. [CAT 2021, Slot 3] In a triangle ABC, angle BCA = 50°. D and E are points on AB and AC, respectively, such that AD = DE. If F is a point on BC such that BD = DF, find angle FDE (in degrees). (P)
(a) 65
(b) 70
(c) 80
(d) 90
10. [CAT 2023, Slot 2] A triangle is drawn with its vertices on a circle C such that one of its sides is a diameter of C, and the other two sides have lengths in the ratio a:b. If the radius of the circle is r, find the area of the triangle. (P)
(a) abr²/(a²+b²)
(b) 2abr²/(a²+b²)
(c) abr²/(2(a²+b²))
(d) 4abr²/(a²+b²)
11. [CAT 2025, Slot 3] ABCD is a trapezium in which AB is parallel to DC, AD is perpendicular to AB, and AB = 3DC. If a circle inscribed in the trapezium (touching all four sides) has a radius of 3 cm, find the area, in sq cm, of the trapezium. (P)
(a) 36√2
(b) 30√3
(c) 48
(d) 54
12. [CAT 2022, Slot 3] In a triangle ABC, AB = AC = 8 cm. A circle drawn with BC as diameter passes through A. Another circle, centred at A, passes through B and C. Find the area, in sq cm, of the overlapping region between the two circles. (P)
(a) 16π − 16
(b) 32π − 32
(c) 24π − 16
(d) 32π − 16
Scroll to the bottom for answer key and refer embeded video page for solution or visit @iimwalabanda YouTube page
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