Geometry 1 Club 100

Geometry - 1
1. In the figure given below, AB is the diameter of the larger circle while three
smaller circles are drawn inside this circle such that their diameters are along
AB. The radius of each of these three circles is 1 cm and the length of AB is 6
cm. Another circle with center at R is drawn which touches the two smaller
circles and the larger circle. Find the length of the radius (in cm) of this circle?
(a) √3/2 (b) 1/√2 (c) 1 (d) None of these
2. ABCD is a parallelogram. CD is extended to G. BG intersects AC and AD at

point E and point F respectively. If BE = 24 units and EF = 18 units, then what
is the length of FG (in units)?
(a) 6 (b) 12 (c) 14 (d) Data Insufficient
3. The three sides AB, BC and CA of a triangle ABC are 7 cm, 10 cm and 12 cm
long respectively. AB is extended to D and AD = 28 cm. BC is extended to E
and BE = 20 cm. CA is extended to F and CF = 36 cm. What is the ratio of the
area of triangle ABC to the area of triangle DEF?
(a) 1 : 17 (b) 1 : 18 (c) 1 : 9 (d) 1 : 10
4. The adjoining figure shows a square ABCD, with E, F, G and H as the mid-
points of sides AB, BC, CD and DA respectively. AF, BG, CH and DE are joined,
forming a smaller square PQRS inside. What is the ratio of areas of squares
PQRS and ABCD?
(a) 1 : 4 (b) 1: 5 (c) 1 : 6 (d) Cannot be determined
P
5. On the circumference of a circle of radius 5 cm, 3 points P, Q and R are
taken as shown. If l(PQ) = l(PR) = 8 cm, then find l(QR)
(a) 8 cm (b) 8.4 cm (c) 9.6 cm (d) 10.8 cm
Q R
6. A sphere A contains a cube B, which is the largest possible cube that can
fit in A. Within this cube, there is a sphere C, which is the largest possible
sphere that can be contained in B. Find the ratio of the volumes of A and C.
(a) 2√2 : 1 (b) 3√3 : 1 (c) 3√3 : 2√2 (d) 9√3 : 1
7. In the above question, what will be ratios of surface areas of A and C?
(a) 2 : 1 (b) 3 : 2 (c) 3 : 1 (d) 3√3 : 1
IMS Club 100 2024 Geometry

Geometry - 1
8. In a triangle ABC, medians BD and CE are drawn and they intersect at O. What would be the ratio of the
area of quadrilateral ADOE to that of triangle BOC?
(a) 1 : 1 (b) 3 : 4 (c) 1 : 2 (d) Cannot be determined
9. In a square PQRS, T is the midpoint of PQ and U is any variable point on QR. What is the minimum
possible value of ‘SU + UT’ (in cm) if the side of the square is 2 cm?
(a) 2√2 (b) √5 + √2 (c) 1+ 2√2 (d) √13
10. A trapezium has 2 parallel sides as 7 and 25. The diagonals are perpendicular to the non-parallel sides.
What is the area of the trapezium?
(a) 192 (b) 240 (c) 224 (d) 160
11. The diagonals of a regular pentagon ABCDE are drawn to form a star. Find the measure of angle ACE
(a) 24° (b) 30° (c) 36° (d) 45°
12. The midpoints of the four sides of a regular hexagon are joined to form a rectangle. What is the ratio
of the area of the rectangle to that of the hexagon?
(a) 1:2 (b) 1:3 (c) 1: √3 (d) 1: √2
13. A septagon (7-sided figure) has all internal angles as pairwise distinct, obtuse, and multiples of 9. What
is the sum of the two largest angles?
(a) 300° (b) 315° (c) 333° (d) 297
14. In a regular octagon ABCDEFH, if the length of AC is x and that of AE is y then the ratio x : y is
(a) 1 : 2 (b) 2: √5 (c) 1: √3 (d) 1: √2
15. A regular nonagon ABCDEFGHI is inscribed in a circle. Z lies somewhere on minor arc AB. Find m∠AZB
(a) 154° (b) 160° (c) 162° (d) 165°
16. Using the 10 vertices of a regular decagon, how many non-right-angled triangles can be made?
(a) 120 (b) 100 (c) 80 (d) 60

Geometry - 1
17. What will be the shaded area, in square units, in the adjoining figure?
6 cm
(a) 45 (b) 60
12 cm
(c) 40 (d) 50
20 cm
18. An equilateral triangle ABC of side 40 cm is cut into two pieces in such a way that one piece is an
equilateral triangle containing the vertex A and the second piece is a trapezium. Two such trapeziums are
placed beside each other to form a parallelogram. What is the perimeter (in cm) of the parallelogram?
(a) 120 (b) 160 (c) 200 (d) 240
19. The interior angle of an n-sided regular polygon is an integer. If n is an odd number, then how many
values are possible for n?
(a) 3 (b) 5 (c) 14 (d) 6
S T
20. If STUVWXYZ is a regular octagon, and diagonals YU and YV are drawn (as
shown in the figure), then the ratio of the areas A : B will be Z U
(a) 2 : 3 (b) 2√3 : 3 √2 A

Y V
(c) 2 : √2 + 1 (d) 1 : 1 B
X W
21. In triangle PQR, PQ = PR = 10 cm. Points S, T and U lie on PQ, QR and PR respectively such that ST is
parallel to PR and UT is parallel to PQ. What is the perimeter (in cm) of the quadrilateral PSTU?
(a) 18 (b) 20 (c) 24 (d) Data Insufficient
22. ABCD and PQRS are congruent rectangles with l(AB) = l(PQ) = 16 cm and l(BC) = l(QR) = 12 cm. They
are placed partially overlapping each other so that point P coincides with point D and point R coincides
with point B while the other vertices do not coincide. Find the area of the overlapping region.
(a) 96 cm2 (b) 150 cm2 (c) 192 cm2 (d) 75 cm2
23. On the circumference of a circle, n equally spaced points are chosen. The distances between every
possible pair of points are recorded and it is found that there are 10 distinct values for these distances.
What is the maximum possible value of n?
(a) 23 (b) 22 (c) 20 (d) 21
24. In a quadrilateral ABCD, l(AB) = 1, l(BC) = 3, l(CD) = 5, and l(AD) = n, where n ∈ N. Then the number of
possible values of n is
(a) 6 (b) 7 (c) 8 (d) 9

Geometry 1 Club 100

Uploaded by

Copyright:

Available Formats

Geometry 1 Club 100

Uploaded by

Document Information

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

Geometry 1 Club 100

Uploaded by

Copyright:

Available Formats

Geometry - 1

2. ABCD is a parallelogram. CD is extended to G. BG intersects AC and AD at

(a) 2√2 : 1 (b) 3√3 : 1 (c) 3√3 : 2√2 (d) 9√3 : 1

7. In the above question, what will be ratios of surface areas of A and C?

(a) 2 : 1 (b) 3 : 2 (c) 3 : 1 (d) 3√3 : 1

IMS Club 100 2024 Geometry

IMS Club 100 2024 Geometry

(a) 2 : 3 (b) 2√3 : 3 √2 A

IMS Club 100 2024 Geometry

You might also like