MCQ Questions on Geometry for Competitive Exams Page-7 section-2

Section 1 Section 2 Section 3

61.
Let D and E be two points on the side BC of ΔABC such that AD = AE and ∠BAD = ∠EAC. If AB = (3x + 1) cm, BD = 9 cm, AC = 34 cm and EC = (y + 1) cm, then the value of (x + y) is:

A. 19

B. 16

C. 17

D. 20

Answer & Solution Discuss in Board Save for Later

62.
In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY?

A. $$4\sqrt {10} $$

B. $$2\sqrt {10} $$

C. $$6\sqrt {10} $$

D. $$3\sqrt 5 $$

Answer & Solution Discuss in Board Save for Later

63.
ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true?

A. BP = PC

B. BP > PC

C. BP < PC

D. BP = $$\frac{1}{2}$$PC

Answer & Solution Discuss in Board Save for Later

64.
AB is a diameter of a circle with centre O, CB is a tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 6 cm and AG = 8 cm, then the length of BC is:

A. 2√5 cm

B. 6√6 cm

C. 2√6 cm

D. 6√5 cm

Answer & Solution Discuss in Board Save for Later

65.
A circle is inscribed in a triangle ABC. It touches side AB, BC and AC at points R, P and Q, respectively. If AQ = 2.6 cm, PC = 2.7 cm and BR = 3 cm, then the perimeter (in cm) of the triangle ΔABC is:

A. 28

B. 30

C. 16.6

D. 33.2

Answer & Solution Discuss in Board Save for Later

66.
PQR is a triangle. S and T are the midpoints of the sides PQ and PR respectively. which of the following is TRUE?
I. Triangle PST is similar to triangle PQR.
II. ST = $$\frac{1}{2}$$ (QR)
III. ST is parallel to QR.

A. Only I and II

B. Only II and III

C. Only I and III

D. All I, II and III

Answer & Solution Discuss in Board Save for Later

67.
B₁ is a point on the side AC of ΔABC and B₁B is joined. A line is drawn through A parallel to B₁B meeting BC at A₁ and another line is drawn through C parallel to B₁B meeting AB produced at C₁. Then

A. $$\frac{1}{{{\text{C}}{{\text{C}}_1}}} - \frac{1}{{{\text{A}}{{\text{A}}_1}}} = \frac{1}{{{\text{B}}{{\text{B}}_1}}}$$

B. $$\frac{1}{{{\text{C}}{{\text{C}}_1}}} + \frac{1}{{{\text{A}}{{\text{A}}_1}}} = \frac{1}{{{\text{B}}{{\text{B}}_1}}}$$

C. $$\frac{1}{{{\text{B}}{{\text{B}}_1}}} - \frac{1}{{{\text{A}}{{\text{A}}_1}}} = \frac{1}{{{\text{C}}{{\text{C}}_1}}}$$

D. $$\frac{1}{{{\text{B}}{{\text{B}}_1}}} + \frac{1}{{{\text{A}}{{\text{A}}_1}}} = \frac{1}{{{\text{C}}{{\text{C}}_1}}}$$

Answer & Solution Discuss in Board Save for Later

68.
In a circle with centre O, ABCD is a cyclic quadrilateral and AC is the diameter. Chords AB and DC are produced to meet at E. If ∠CAE = 34° and ∠E = 30°, then ∠CBD is equal to:

A. 24°

B. 36°

C. 26°

D. 34°

Answer & Solution Discuss in Board Save for Later

69.
G is the centroid of the triangle ABC. where AB, BC and CA are 7 cm, 24 cm and 25 cm respectively. than BG is:

A. $$6\frac{1}{3}{\text{ cm}}$$

B. $$8\frac{1}{3}{\text{ cm}}$$

C. $$5\frac{1}{2}{\text{ cm}}$$

D. $$4\frac{1}{6}{\text{ cm}}$$

Answer & Solution Discuss in Board Save for Later

70.
Two circles touch externally. The sum of their areas is 130π sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is:

A. 2 cm

B. 3 cm

C. 4 cm

D. 5 cm

Answer & Solution Discuss in Board Save for Later

1 2 3 4 5 6 7 8 9 10

MCQ Questions on Geometry for Competitive Exams

61. Let D and E be two points on the side BC of ΔABC such that AD = AE and ∠BAD = ∠EAC. If AB = (3x + 1) cm, BD = 9 cm, AC = 34 cm and EC = (y + 1) cm, then the value of (x + y) is:

Answer & Solution

62. In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY?

Answer & Solution

63. ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true?

Answer & Solution

64. AB is a diameter of a circle with centre O, CB is a tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 6 cm and AG = 8 cm, then the length of BC is:

Answer & Solution

65. A circle is inscribed in a triangle ABC. It touches side AB, BC and AC at points R, P and Q, respectively. If AQ = 2.6 cm, PC = 2.7 cm and BR = 3 cm, then the perimeter (in cm) of the triangle ΔABC is:

Answer & Solution

66. PQR is a triangle. S and T are the midpoints of the sides PQ and PR respectively. which of the following is TRUE? I. Triangle PST is similar to triangle PQR. II. ST = $$\frac{1}{2}$$ (QR) III. ST is parallel to QR.

Answer & Solution

67. B1 is a point on the side AC of ΔABC and B1B is joined. A line is drawn through A parallel to B1B meeting BC at A1 and another line is drawn through C parallel to B1B meeting AB produced at C1. Then

Answer & Solution

68. In a circle with centre O, ABCD is a cyclic quadrilateral and AC is the diameter. Chords AB and DC are produced to meet at E. If ∠CAE = 34° and ∠E = 30°, then ∠CBD is equal to:

Answer & Solution

69. G is the centroid of the triangle ABC. where AB, BC and CA are 7 cm, 24 cm and 25 cm respectively. than BG is:

Answer & Solution

70. Two circles touch externally. The sum of their areas is 130π sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is:

Answer & Solution

Read More Section(Geometry)

61.
Let D and E be two points on the side BC of ΔABC such that AD = AE and ∠BAD = ∠EAC. If AB = (3x + 1) cm, BD = 9 cm, AC = 34 cm and EC = (y + 1) cm, then the value of (x + y) is:

62.
In the given figure, PQRS is a square inscribed in a circle of radius 4 cm. PQ is produced till point Y. From Y a tangent is drawn to the circle at point R. What is the length (in cm) of SY?

63.
ABC is an isosceles triangle where AB = AC which is circumscribed about a circle. If P is the point where the circle touches the side BC, then which of the following is true?

64.
AB is a diameter of a circle with centre O, CB is a tangent to the circle at B. AC intersects the circle at G. If the radius of the circle is 6 cm and AG = 8 cm, then the length of BC is:

65.
A circle is inscribed in a triangle ABC. It touches side AB, BC and AC at points R, P and Q, respectively. If AQ = 2.6 cm, PC = 2.7 cm and BR = 3 cm, then the perimeter (in cm) of the triangle ΔABC is:

66.
PQR is a triangle. S and T are the midpoints of the sides PQ and PR respectively. which of the following is TRUE?
I. Triangle PST is similar to triangle PQR.
II. ST = $$\frac{1}{2}$$ (QR)
III. ST is parallel to QR.

67.
B₁ is a point on the side AC of ΔABC and B₁B is joined. A line is drawn through A parallel to B₁B meeting BC at A₁ and another line is drawn through C parallel to B₁B meeting AB produced at C₁. Then

68.
In a circle with centre O, ABCD is a cyclic quadrilateral and AC is the diameter. Chords AB and DC are produced to meet at E. If ∠CAE = 34° and ∠E = 30°, then ∠CBD is equal to:

69.
G is the centroid of the triangle ABC. where AB, BC and CA are 7 cm, 24 cm and 25 cm respectively. than BG is:

70.
Two circles touch externally. The sum of their areas is 130π sq cm and the distance between their centres is 14 cm. The radius of the smaller circle is: