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MCQ Questions on Geometry for Competitive Exams

Prepare for competitive exams with our Geometry MCQ questions. Practice essential theorems and problem-solving techniques with questions tailored to exam patterns. Page-6 section-3

Each section contains 100 MCQs on Geometry .
51
ln a quadrilateral ABCD, E is a point in the interior of the quadrilateral such that DE and CE are the bisectors of ∠D and ∠C, respectively. If ∠B = 82° and ∠DEC = 80°, then ∠A = ?
Discuss
Answer & Solution
Answer: Option D
Solution:
Geometry mcq question image
α + β = 100°
2(α + β) = 200°
360° = 282° + ∠A
∠A = 78°
52
In the following figure, P and Q are centres of two circles. The circles are intersecting at points A and B. PA produced on both the sides meets the circles at C and D. If ∠CPB = 100°, then find the value of x.
Geometry mcq question image
Discuss
Answer & Solution
Answer: Option D
Solution:
Geometry mcq question image
∠CPB = 100°
AB draw,
PA = PB = Radius
∴ ∠PAB = ∠PBA
∠CPB = ∠PAB + ∠PBA (Exterior angle)
⇒ 2∠PAB = 100°
∴ ∠PAB = 50°
∠BAD = 180° - 50° = 30°
Reflex ∠BQD = 2 × 130° = 260°
∴ x = 360° - 260° = 100°
53
AC is the diameter of a circle dividing the circle into two semicircles. ED is a chord in one semicircle, such that ED is parallel to AC. B is a point on the circumference of the circle in the other semicircle. ∠CBE = 75°. What is the measure (in degree) of ∠CED?
Discuss
Answer & Solution
Answer: Option D
No explanation is given for this question. Let's Discuss on Board
54
In an equilateral ΔABC, the medians AD, BE and CF intersect to each other at point G. If the area of quadrilateral BDGF is 12√3 cm2, then the side of ΔABC is:
Discuss
Answer & Solution
Answer: Option D
Solution:
Geometry mcq question image
$$\eqalign{ & 2{\text{ unit}} \to 12\sqrt 3 \cr & 6{\text{ unit}} \to 12\sqrt 3 \times 3 = 36\sqrt 3 \cr & {\text{Area}} = \frac{{\sqrt 3 }}{4}{a^2} \cr & 36\sqrt 3 = \frac{{\sqrt 3 }}{4}{a^2} \cr & a = 12{\text{ cm}} \cr} $$
55
In ΔABC, D and E are the midpoints of sides BC and AC, respectively, AD and BE intersect at G at right angle. If AD = 18 cm and BE = 12 cm, then the length of DC (in cm) is:
Discuss
Answer & Solution
Answer: Option A
Solution:
Geometry mcq question image
AD = 18
BE = 12
BO = 8
DG = 6
ΔDGB
Geometry mcq question image
82 + 62 = BD2
BD = 10
BD = CD = 10
56
Two circles with centres A and B of radii 5 cm and 3 cm respectively touch each other internally. If the perpendicular bisector of AB meets the bigger circle at P and Q, then the value of PQ is
Discuss
Answer & Solution
Answer: Option D
Solution:
According to question
Geometry mcq question image
AP = 5 cm, DB = 3 cm
AB = 5 - 3 = 2 cm
AO = AB ÷ 2 = 1 cm
PQ is ⊥ bisector
∴ AO = 1, PO = OQ
In right angle ΔPOA
(AP)2 = (OA)2 + (OP)2
(5)2 = (1)2 + (OP)2
(OP)2 = 25 - 1
(OP)2 = 24
(OP) = 2√6 cm
∴ PQ = 2 × OP
PQ = 2 × 2√6
PQ = 4√6 cm
57
In ΔPQR, ∠Q = 84° and ∠R = 48°, PS ⊥ QR at S and the bisector of ∠P meets QR at T. What is the measure of ∠SPT ?
Discuss
Answer & Solution
Answer: Option D
Solution:
Geometry mcq question image
∠QPR = 180° - (84° + 48°) = 48°
∠QPT = $$\frac{{{{48}^ \circ }}}{2}$$ = 24°
∠QPS = 6°
∠SPT + ∠SPQ = 24°
∠SPT + 6° = 24°
∠SPT = 18°
58
In ΔPQR, ∠P = 90°. S and T are the mid points of sides PR and PQ, respectively. What is the value of $$\frac{{{\text{R}}{{\text{Q}}^2}}}{{{\text{Q}}{{\text{S}}^2} + {\text{R}}{{\text{T}}^2}}} = ?$$
Discuss
Answer & Solution
Answer: Option B
Solution:
Geometry mcq question image
$$\eqalign{ & {\text{RT }}\& {\text{ QS are medians}} \cr & 5{\text{Q}}{{\text{R}}^2} = 4\left( {{\text{Q}}{{\text{S}}^2} + {\text{R}}{{\text{T}}^2}} \right) \cr & \Rightarrow \frac{4}{5} = \frac{{{\text{Q}}{{\text{R}}^2}}}{{{\text{Q}}{{\text{S}}^2} + {\text{R}}{{\text{T}}^2}}} \cr} $$
59
In a triangle ABC, AB = AC and the perimeter of ΔABC is 8(2 + √2) cm. If the length of BC is √2 times the length of AB, then find the area of ΔABC.
Discuss
Answer & Solution
Answer: Option A
Solution:
Geometry mcq question image
Let the side of triangle be x, x & √2x
Perimeter = 8(2 + √2)
x + x + x√2 = 8(2 + √2)
2x + x√2 = 8(2 + √2)
x(2 + √2) = 8(2 + √2)
(comparing on both side)
x = 8
Area of ΔABC = $$\frac{1}{2}$$ × 8 × 8 = 4 × 8
= 32
60
Which of the set of three sides can't form a triangle?
Discuss
Answer & Solution
Answer: Option B
Solution:
Fora triangle sum of 2 sides is always greater than the third side.
Hence, combination (5, 8, 15) never be possible.