Download App

Maths Assertion (A) & Reason (B) MCQ

Circles [NEW] · Gujarat Board (GSEB) STD 9 (GSEB - English Medium). 14 questions.

Questions

Assertion (A) & Reason (B) MCQ

🎯

Test yourself on this topic

14 questions · timed · auto-graded

MCQ 11 Mark
Statement-1 (A): Two chords of a circle of lengths 10 cm and 8 cm are at the distance 8 cm and 3.5 cm, respectively from the centre.
Statement-2 (R): Of any two chords of a circle the one which is larger is nearer to the centre.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • ✓
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: D.
Statement-1 is False, Statement-2 is True.
(d)
Statement-2 is true. Statement-1 is not true as the larger chord is at smaller distance from the centre. Hence, option (d) is correct.
View full question & answer→
MCQ 21 Mark
Statement-1 (A): The angles subtended by a chord at any two points of a circle are equal.
Statement-2 (R): Angles in the same segment of a circle are equal.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • ✓
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: D.
Statement-1 is False, Statement-2 is True.
(d)
Statement-2 is true.
Statement-1 is not true, because the angles subtended by a chord at any two points on the circle will be equal if two points lie in the same segment (major or minor) only. Hence, option (d) is correct.
View full question & answer→
MCQ 31 Mark
Statement-1 (A): In Fig. $O$ is the centre of a circle and $\angle A O C=140^{\circ}$, then $\angle A B C=110^{\circ}$.
Statement-2 (R): Angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Image
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
b
View full question & answer→
MCQ 41 Mark
Statement-1 (A): In Fig.(i), if AOB is a diameter and $\angle A D C=120^{\circ}$, then $\angle C A B=30^{\circ}$.
Statement-2 (R): In Fig.(ii), AOB is a diameter and $\angle A D C=120^{\circ}$, then $\angle B A C=30^{\circ}$.
Image
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(a)
In Fig. (ii), ABCD is a cyclic quadrilateral such that $\angle A D C=120^{\circ}$. Therefore,
$\angle A D C+\angle A B C=180^{\circ} \Rightarrow \angle A BC=180^{\circ}-120^{\circ}=60^{\circ}$
We find that $\angle A C B=90^{\circ}$ (angle in a semi-circle).
Using angle sum property in $\triangle A C B$, we obtain
$\angle A C B+\angle B A C+\angle A B C=180^{\circ} \Rightarrow 90^{\circ}+\angle B AC+60^{\circ}=180^{\circ} \Rightarrow \angle B A C=30^{\circ}$
So, statement-2 is true.
In Fig.(i), join BC. We observe that ABCD is a cyclic quadrilateral.
$\therefore \quad \angle A D C+\angle A B C=180^{\circ} \Rightarrow 120^{\circ}+\angle A BC=180^{\circ} \Rightarrow \angle A B C=60^{\circ}$
Since AOB is a diameter of the circle. Therefore, $\angle A C B=90^{\circ}$.
Using angle sum property in $\triangle A B C$, we obtain $\angle C A B=30^{\circ}$.
So, statement- 1 is also true. We also observe that statement- 2 is a correct explanation for statement-1. Hence, option (a) is correct.
View full question & answer→
MCQ 51 Mark
Statement-1 (A): In Fig. if $\angle A O B=100^{\circ}$ and $\angle B O C=120^{\circ}$, then $\angle A B C=70^{\circ}$.
Statement-2 (R): The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
Image
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
View full question & answer→
MCQ 61 Mark
Statement-1 (A): In Fig. ABCD is a cyclic quadrilateral. If $A B \| D C$ and $\angle A=80^{\circ}$, then $\angle B=80^{\circ}, \angle C=\angle D=100^{\circ}$.
Statement-2 (R): The sum of each pair of opposite angles of a cyclic quadrilateral is $180^{\circ}$.
Image
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
View full question & answer→
MCQ 71 Mark
Statement-1 (A): In Fig. AB and CD are two equal chords of a circle with centre O. If $O P \perp A B$ and $O Q \perp C D$ and $\angle P O Q=110^{\circ}$, then $\angle A P Q=35^{\circ}$.
Statement-2 (R): Chords on the opposite side of the centre of a circle are equal.
Image
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: C.
Statement-1 is true, Statement-2 is false.
c
View full question & answer→
MCQ 81 Mark
Statement-1 (A): If two chords AB and CD of a circle are each at a distance 4 cm from the centre, then AB = CD.
Statement-2 (R): Chords equidistant from the centre of a circle are equal in length.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(a)
Statement-2 is true. Using statement-2, we find that statement-1 is also true. Also, statement-2 is a correct explanation for statement-1.
View full question & answer→
MCQ 91 Mark
Statement-1 (A): If P, Q, R, S are four points such that $\angle Q P R=40^{\circ}$ and $\angle Q S R=80^{\circ}$, then $S$ is the centre of the circle through Q, R and P.
Statement-2 (R): If A, B, C and D are four points such that $\angle B A C=60^{\circ}$ and $\angle B D C=60^{\circ}$, then A, B, C, D are concyclic points.
  • A
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: B.
Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
b
View full question & answer→
MCQ 101 Mark
Statement-1 (A): If POQ is a diameter of a circle and R is a point on the circle then $\operatorname{ar}(\triangle P Q R)=\frac{1}{2}(P R \times Q R)$
Statement-2 (R): Angle is a semi-circle is a right angle.
  • ✓
    Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is true, Statement-2 is false.
  • D
    Statement-1 is false, Statement-2 is true.
Answer
Correct option: A.
Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
a
View full question & answer→
MCQ 111 Mark
Statement-1 (A): If AOB is a diameter of a circle and C is a point on the circle, then $A C^2+B C^2=A B^2$
Statement-2 (R): Angle is a semi-circle is a right angle.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: A.
Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
(a)
Statement-2 is true. Using statement- 2, we find that $\angle A C B=90^{\circ}$. Applying Pythagoras theorem in $\triangle A C B$, we obtain $A B^2=A C^2+B C^2$. So, statement -1 is also true.
Clearly, statement-2 is a correct explanation for statement- 1. Hence, option (a) is correct.
View full question & answer→
MCQ 121 Mark
Statement-1 (A): If A, B, C, D are four points such that $\angle B A C=30^{\circ}$ and $\angle B D C=60^{\circ}$, then D is the centre of the circle through A, B and C.
Statement-2 (R): The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • ✓
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: D.
Statement-1 is False, Statement-2 is True.
(d)
Statement-2 is true.
Statement-1 is not true, because there can be many points D such that $\angle B D C=60^{\circ}$ and each such point cannot be the centre of the circle through A, B, C. Hence, option (d) is correct.
View full question & answer→
MCQ 131 Mark
Statement-1 (A): If A, B, C and D are four points such that $\angle B A C=45^{\circ}$ and $\angle B D C=45^{\circ}$, then A, B, C, D are concyclic.
Statement-2 (R): ABCD is a cyclic quadrilateral such that $\angle A=85^{\circ}, \angle B=70^{\circ}$, $\angle C=95^{\circ}$ and $\angle D=110^{\circ}$
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • ✓
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • C
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: B.
Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
(b)
Statement-1 is true, because angles in the same segment of a circle are equal. Statement-2 is also true, because $\angle A+\angle C=180^{\circ}$ and $\angle B+\angle D=180^{\circ}$.
Hence, option (b) is correct.
View full question & answer→
MCQ 141 Mark
Statement-1 (A): A circle of radius 3 cm can be drawn through two points $A, B$ such that $A B=6 cm$.
Statement-2 (R): Through three collinear points a circle can be drawn.
  • A
    Statement-1 and Statement-2 are True; Statement-2 is a correct explanation for Statement-1.
  • B
    Statement-1 and Statement-2 are True; Statement-2 is not a correct explanation for Statement-1.
  • ✓
    Statement-1 is True, Statement-2 is False.
  • D
    Statement-1 is False, Statement-2 is True.
Answer
Correct option: C.
Statement-1 is True, Statement-2 is False.
(c)
Statement- 1 is true, because a circle of radius 3 cm can be drawn which has AB as its diameter. Statement-2 is not true because a circle through two points cannot pass through a point which is collinear to these two points. Hence, option (c) is correct.
View full question & answer→
Generate Paper FreeAll Circles [NEW] topics
Assertion (A) & Reason (B) MCQ - Maths STD 9 Questions - Vidyadip