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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-3 section-1

Each section contains 100 MCQs on Geometry .
21
Two circles intersect each other at the points A and B. A straight line parallel to AB intersects the circles at C, D, E and F. If CD = 4.5 cm, then the measure of EF is?
Discuss
Answer & Solution
Answer: Option C
No explanation is given for this question. Let's Discuss on Board
22
In case of an acute angled triangle, its orthocenter lies
Discuss
Answer & Solution
Answer: Option A
Solution:
In acute angled triangle orthocentre is always inside the triangle.
23
AB is a diameter of a circle having centre at O. PQ is a chord which does not intersect AB. Join AP and BQ. If ∠PAB = ∠ABQ, then ABQP is a:
Discuss
Answer & Solution
Answer: Option C
No explanation is given for this question. Let's Discuss on Board
24
In a circle with centre O, BC is a chord. Point D and A are on the circle, on the opposite side of BC, such that ∠DBC = 28° and BD = DC. What is the measure of ∠BOC?
Discuss
Answer & Solution
Answer: Option C
Solution:
Geometry mcq question image
∠DBC = 28°   (Given)
BD = DC,   (Given)
∠BCD = 28°
So, ∠BDC = 180° - (28° + 28°) = 124°
∠BAC = 180° - 124° = 56°
(Cyclic $$\square $$)
∠BOC = 2 × ∠BAC = 56° × 2 = 112° Answer.
25
Given that ΔDEF ∽ ΔABC, if the area of ΔABC is 9 cm2 and that of ΔDEF = 12 cm2 and BC = 2.1 cm, then the length of EF is:
Discuss
Answer & Solution
Answer: Option B
No explanation is given for this question. Let's Discuss on Board
26
The measure of one of the exterior angles of a triangle is twice one of the interior opposite angles and the measure of the other interior opposite angles is 60°. The triangle is a/an:
Discuss
Answer & Solution
Answer: Option D
Solution:
Geometry mcq question image
2x = x + 60°
x = 60°
This triangle is a equilateral triangle.
27
In ΔXYZ, L and M are the mid points of the sides XY and XZ, respectively. R is a point on the segment LM, such that LR : RM = 1 : 2. If LR = 3 cm, then YZ is equal to:
Discuss
Answer & Solution
Answer: Option C
Solution:
Geometry mcq question image
1 unit → 3 cm
3 unit → 9 cm
YZ = 2LM = 2 × 9 = 18 cm
28
In ΔABC, D and E are the mid points of sides BC and AC, respectively. If AD = 10.8 cm, BE = 14.4 cm and AD and BE intersect at G at a right angle, then the area (in cm2) of ΔABC is:
Discuss
Answer & Solution
Answer: Option A
No explanation is given for this question. Let's Discuss on Board
29
A triangle has sides 25, 39, 34 units. If the area of a square exceeds the area of this triangle by 21 units, then the side of the square is:
Discuss
Answer & Solution
Answer: Option B
Solution:
Geometry mcq question image
$$\eqalign{ & s = \frac{{25 + 34 + 39}}{2} = 49 \cr & {\text{Area of }}\Delta ABC = \sqrt {s\left( {s - a} \right)\left( {s - b} \right)\left( {s - c} \right)} \cr & = \sqrt {49 \times 15 \times 10 \times 24} \cr & = \sqrt {{s^2} \times 3 \times 2 \times {2^3} \times 3} \cr & = 7 \times 5 \times 3 \times 4 \cr & = 420 \cr} $$
So, area of square is 21 more than area of Δ = (i.e.)
= 420 + 21 = 441 square unit
$$\eqalign{ & {{\text{A}}^2} = 441 \cr & {\text{A}} = {\left[ {{{\left( {21} \right)}^2}} \right]^{\frac{1}{2}}} = 21 \cr} $$
30
Two circles touch externally at P. QR is a common tangent of the circles touching the circles at Q and R. Then measure of ∠QPR is
Discuss
Answer & Solution
Answer: Option C
Solution:
According to question
Geometry mcq question image
QR is the common tangent and NO is also the common tangent.
∴ QN = NP = NR
In ΔQPN
∠NQP = ∠NPQ
∠NRP = ∠NPR
In ΔPQR
∠P + ∠Q + ∠R = 180°
x + y + x + y = 180°
2x + 2y = 180°
x + y = 90°
As shown in the figure x + y = ∠P = 90°