Geometry MCQs for Competitive Examination
Solve the following problems.
Q. 1
In a circle with centre O, AD is a diameter, and AC is a chord. B is a point on AC, such that OB = 5 cm and ∠OBA =60°. If ∠DOC = 60°, then what is the length of BC?
(A) 4 cm
(B) 3√5 cm
(C) 5√3 cm
(D) 5 cm
Answer: (D) 5 cm
Explanation:
Q. 2
Tangents AB and AC are drawn to a circle from a point A, such that ∠BAC =40°. A chord CP is drawn parallel to BA. The measure of ∠CBP is
(A) 55°
(B) 35°
(C) 45°
(D) 40°
Answer: (D) 40°
Explanation:
Q. 3
The sides AB and AC of ΔABC are produced to point D and E, respectively. The bisectors of ∠CBD and ∠BCE meet at P. If ∠A = 72°, then the measure of ∠P is
(A) 36°
(B) 45°
(C) 60°
(D) 54°
Answer: (D) 54°
Explanation:
Q. 4
In ΔABC, D is a point on side AB such that BD = 2 cm and DA = 3 cm. E is a point on BC such that DE||AC, and AC= 4 cm. Then (Area of ΔBDE) : (Area of trapezium ACED) is:
(A) 4 : 21
(B) 2 : 5
(C) 1 : 5
(D) 4 : 25
Answer: (A) 4 : 21
Explanation:
Q. 5
The radius of two concentric circles are 15 cm and 9 cm. What is the length of the chord of the larger circle which is tangent to the smaller circle?
(A) 24 cm
(B) 18 cm
(C) 20 cm
(D) 25 cm
Answer: (A) 24 cm
Explanation:
Q. 6
In triangle ABC, D and E are the points on sides AB and AC, respectively, such that DE|| BC. If DE : BC =3 : 5, then (Area of triangle ADE) : (Area of quadrilateral DECB) is
(A) 9:16
(B) 3:4
(C) 9:25
(D) 5:8
Answer: (A) 9:16
Explanation:
Q. 7
In ΔABC, AB = 7 cm, BC = 24 cm and AC = 25 cm. If G is the centroid of the triangle, then what is the length (in cm) of BG?
(A) 10
(B) 8(1/3)
(C) 8(2/3)
(D) 9
Answer: (B) 8(1/3)
Explanation:
Q. 8
Two circles of radii 15 cm and 12 cm intersect each other, and the length of their common chord is 18 cm. What is the distance (in cm) between their centres?
(A) 18+√7
(B) 15+√7
(C) 12+2√7
(D) 12+3√7
Answer: (D) 12+3√7
Explanation:
Q. 9
ABCD is a cyclic quadrilateral such that AB is a diameter of the circle circumscribing it and ∠ADC = 158°. Then ∠BAC is equal to:
(A) 50°
(B) 38°
(C) 68°
(D) 40°
Answer: (C) 68°
Explanation:
Q. 10
In ΔABC, the bisectors of ∠B and ∠C intersect each other at a point D. If ∠BDE = 104°, then the measure of ∠A is
(A) 28°
(B) 32°
(C) 30°
(D) 26°
Answer: (A) 28°
Explanation:
Q. 11
In ΔABC, D and E are the points on sides AC and AB, respectively, such that ∠ADE = ∠B. If AD = 7.6 cm, AE = 7.2 cm, BE = 4.2 and BC = 8.4 cm, then DE is equal to
(A) 6.3 cm
(B) 5.8 cm
(C) 7.4 cm
(D) 5.6 cm
Answer: (D) 5.6 cm
Explanation:
Q. 12
PAT is a tangent to a circle at point A on it, and AB is a chord such that ∠BAT = 72°. If C is a point on the circle such that ∠CBA = 58°, then what is the measure of ∠CAB?
(A) 50°
(B) 62°
(C) 48°
(D) 60°
Answer: (A) 50°
Explanation;
Q. 13
The vertices A, B, C, and D of a quadrilateral ABCD lie on a circle. ∠A is thrice ∠C and ∠D is twice ∠B. What is the difference between the measures of ∠B and ∠C?
(A) 15°
(B) 28°
(C) 18°
(D) 20°
Answer: (A) 15°
Explanation:
Q. 14
Let ΔABC ∼ ΔQPR and area(ΔABC):area(ΔPQR)=9:16. If AB = 12 cm, BC = 6 cm and AC = 9 cm, then QP is equal to
(A) 16 cm
(B) 9 cm
(C) 12 cm
(D) 8 cm
Answer: (A) 16 cm
Explanation:
Q. 15
A circle is inscribed in a quadrilateral ABCD, touching sides AB, BC, CD and DA at P, Q, R and S, respectively. If AS= 8 cm, BC = 11 cm, and CR = 5 cm, then the length AB is equal to
(A) 12 cm
(B) 13 cm
(C) 16 cm
(D) 14 cm
Answer: (D) 14 cm
Explanation:
Q. 16
In ABC, AD ⊥ BC at D and AE is the bisector of ∠A. If ∠B = 72° and ∠C = 26°, then what is the measure of ∠DAE?
(A) 23°
(B) 25°
(C) 49°
(D) 37°
Answer: (A) 23°
Explanation:
Q. 17
In a circle, chords AB and CD intersect each other at E. If CD = 18 cm, DE = 6 cm and AE = 18 cm, then BE = ?
(A) 6 cm
(B) 8 cm
(C) 3 cm
(D) 4 cm
Answer: (D) 4 cm
Explanation:
Q. 18
In ΔABC, ΔA = 90°. If BL and CM are the medians, then
(A) 4 (BL² + CM²) = 3 BC²
(B) 4 (BL² + CM²) = 5 BC²
(C) 3 (BL² + CM²) = 4 BC²
(D) 5 (BL² + CM²) = 4 BC²
Answer: (B) 4(BL² + CM²) = 5BC²
Explanation:
Q. 19
PQRS is a cyclic quadrilateral. If P is four times ∠R and ∠S is three times ∠Q, then the sum of ∠Q and ∠R is
(A) 77°
(B) 73°
(C) 81°
(D) 86°
Answer: (C) 81°
Explanation:
Q. 20
In ∆ABC, BD ⊥ AC. E is a point on BC such that ∠BEA = If ∠EAC = 38° and ∠EBD = 40°, then the value of x is
(A) 88°
(B) 68°
(C) 78°
(D) 72°
Answer: (A) 88°
Explanation: