Geometry Questions and Answers for Your Practice
The lengths of the lengths placed on the sides of a point inside an equilateral triangle are 6 cm, 8 cm and 10 cm. What is the area of the triangle?
(A) $$ {48\ cm^{2}}$$
(B) $$ {16\sqrt{3}}\ cm^{2}$$
(C) $$ {192\sqrt{3}}\ cm^{2}$$
(D) $$ {192 \ cm^{2}}$$
Correct Answer : C
ΔABC and ΔDBC are on the same base BC but on opposite sides of it. AD and BC intersect each other O. If AO=a cm, DO=b cm and the area of ΔABC= x cm2, then what is the area (in cm2) of ΔDBC?
(A) $${ab\over 2}{x}$$
(B) $${a\over b}{x}$$
(C) $${b\over a}{x}$$
(D) $${a+b\over2}{x}$$
Correct Answer : C
Find the area of the largest triangle made in a semicircle of r cm radius?
(A) $$ {2r \ cm^{2}}$$
(B) $$ {r^{2} \ cm^{2}}$$
(C) $$ {2\ cm^{2}}$$
(D) $$ {1\over 2}{r^{2}}\ {cm^{2}}$$
Correct Answer : B
The sides of a triangle are 56 cm, 90 cm and 106 cm. The circumference of its circumcircle is:
(A) 108 π
(B) 112 π
(C) 106 π
(D) 109 π
Correct Answer : C
The sum of all interior angles of a regular polygon is twice the sum of all its exterior angles. The number of sides of the polygon is
(A) 6
(B) 8
(C) 12
(D) 10
Correct Answer : A
In the given figure, ABC is an equilateral triangle. Two circles of radius 4 cm and 12 cm are inscribed in the triangle. What is the side (in cm) of an equilateral triangle?
(A) $$ {32\over \sqrt{3}}$$
(B) $$ {64\sqrt{3}}$$
(C) $$ {32\sqrt{3}}$$
(D) $$ {24\sqrt{3}}$$
Correct Answer : D
The area of a circle is proportional to the square of its radius. A small circle of radius 3 cm is drawn within a larger circle of radius 5 cm. Find the ratio of the difference between the area of the larger circle and that of the smaller circle to the area of the larger circle.
(A) 16: 25
(B) 9: 25
(C) 9:16
(D) 16: 27
Correct Answer : A
Rectangle ABCD is formed in a circle with centre D. IF AE=6 cm and AD=9 cm, then find the perimeter of the rectangle. 
(A) 42 cm
(B) 45 cm
(C) 48 cm
(D) None of these
Correct Answer : A
In the given figure, PQRS is a square of side 20 cm and SR is extended to point T. If the length of QT is 25 cm, then what is the distance (in cm) between the centres O1 and O2 of the two circles?
(A) $$ 4{\sqrt{10}}$$
(B) $$ 5{\sqrt{10}}$$
(C) $$ 8{\sqrt{10}}$$
(D) 5
Correct Answer : B
If the perimeter of an equilateral triangle is 18 cm, then length of each median is
(A) $$ {3\sqrt{2}cm}$$
(B) $$ {2\sqrt{3}cm}$$
(C) $$ {3\sqrt{3}cm}$$
(D) $$ {2\sqrt{2}cm}$$
Correct Answer : C
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Vikram Singh
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