Home / Class 9 Math / Ch 10 Circles- MCQ Online Test 1 Class 9 Maths
Chapter 10 Circles- MCQ Online Test 1 Class 9 Maths
1. The center of the circle lies in______ of the circle.
(a) Interior
(b) Exterior
(c) Circumference
(d) None of the above
2. The longest chord of the circle is:
(a)Radius
(b) Arc
(c) Diameter
(d) Segment
3. Equal _____ of the congruent circles subtend equal angles at the centers.
(a) Segments
(b) Radii
(c) Arcs
(d) Chords
4. If chords AB and CD of congruent circles subtend equal angles at their centres, then:
(a) AB = CD
(b) AB > CD
(c) AB < AD
(d) None of the above
5. If there are two separate circles drawn apart from each other, then the maximum number of common points they have:
(a) 0
(b) 1
(c) 2
(d) 3
6. The angle subtended by the diameter of a semi-circle is:
(a) 90
(b) 45
(c) 180
(d) 60
7. If AB and CD are two chords of a circle intersecting at point E, as per the given figure. Then:
(a) ∠BEQ > ∠CEQ
(b) ∠BEQ = ∠CEQ
(c) ∠BEQ < ∠CEQ
(d) None of the above
8. If a line intersects two concentric circles with centre O at A, B, C and D, then:
(a) AB = CD
(b) AB > CD
(c) AB < CD
(d) None of the above
9. In the below figure, the value of ∠ADC is:
(a) 60°
(b) 30°
(c) 45°
(d) 55°
10. In the given figure, find angle OPR.
(a) 20°
(b) 15°
(c) 12°
(d) 10°
Circle class - 9 MCQ - 1
Time limit: 0
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Question 1 of 10
1. Question
The center of the circle lies in______ of the circle.
Correct
Incorrect
Question 2 of 10
2. Question
The longest chord of the circle is:
Correct
Incorrect
Question 3 of 10
3. Question
Equal _____ of the congruent circles subtend equal angles at the centers.
Correct
Explanation: See the figure below:
Let ΔAOB and ΔCOD are two triangles inside the circle.
OA = OC and OB = OD (radii of the circle)
AB = CD (Given)
So, ΔAOB ≅ ΔCOD (SSS congruency)
∴ By CPCT rule, ∠AOB = ∠COD.
Hence, this prove the statement.
Incorrect
Explanation: See the figure below:
Let ΔAOB and ΔCOD are two triangles inside the circle.
OA = OC and OB = OD (radii of the circle)
AB = CD (Given)
So, ΔAOB ≅ ΔCOD (SSS congruency)
∴ By CPCT rule, ∠AOB = ∠COD.
Hence, this prove the statement.
Question 4 of 10
4. Question
If chords AB and CD of congruent circles subtend equal angles at their centres, then:
Correct
Explanation: Take the reference of the figure from above question.
In triangles AOB and COD,
∠AOB = ∠COD (given)
OA = OC and OB = OD (radii of the circle)
So, ΔAOB ≅ ΔCOD. (SAS congruency)
∴ AB = CD (By CPCT)
Incorrect
Explanation: Take the reference of the figure from above question.
In triangles AOB and COD,
∠AOB = ∠COD (given)
OA = OC and OB = OD (radii of the circle)
So, ΔAOB ≅ ΔCOD. (SAS congruency)
∴ AB = CD (By CPCT)
Question 5 of 10
5. Question
If there are two separate circles drawn apart from each other, then the maximum number of common points they have:
Correct
Incorrect
Question 6 of 10
6. Question
The angle subtended by the diameter of a semi-circle is:
Correct
Explanation: The semicircle is half of the circle, hence the diameter of the semicircle will be a straight line subtending 180 degrees.
Incorrect
Explanation: The semicircle is half of the circle, hence the diameter of the semicircle will be a straight line subtending 180 degrees.
Question 7 of 10
7. Question
If AB and CD are two chords of a circle intersecting at point E, as per the given figure. Then:
Correct
Explanation:
OM = ON (Equal chords are always equidistant from the centre)
OE = OE (Common)
∠OME = ∠ONE (perpendiculars)
So, ΔOEM ≅ ΔOEN (by RHS similarity criterion)
Hence, ∠MEO = ∠NEO (by CPCT rule)
∴ ∠BEQ = ∠CEQ
Incorrect
Explanation:
OM = ON (Equal chords are always equidistant from the centre)
OE = OE (Common)
∠OME = ∠ONE (perpendiculars)
So, ΔOEM ≅ ΔOEN (by RHS similarity criterion)
Hence, ∠MEO = ∠NEO (by CPCT rule)
∴ ∠BEQ = ∠CEQ
Question 8 of 10
8. Question
If a line intersects two concentric circles with centre O at A, B, C and D, then:
Correct
Explanation: See the figure below:
From the above fig., OM ⊥ AD.
Therefore, AM = MD — 1
Also, since OM ⊥ BC, OM bisects BC.
Therefore, BM = MC — 2
From equation 1 and equation 2.
AM – BM = MD – MC
∴ AB = CD
Incorrect
Explanation: See the figure below:
From the above fig., OM ⊥ AD.
Therefore, AM = MD — 1
Also, since OM ⊥ BC, OM bisects BC.
Therefore, BM = MC — 2
From equation 1 and equation 2.
AM – BM = MD – MC
∴ AB = CD
Question 9 of 10
9. Question
In the below figure, the value of ∠ADC is:
Correct
Explanation: ∠AOC = ∠AOB + ∠BOC
So, ∠AOC = 60° + 30°
∴ ∠AOC = 90°
An angle subtended by an arc at the centre of the circle is twice the angle subtended by that arc at any point on the rest part of the circle.
So,
∠ADC = 1/2∠AOC
= 1/2 × 90° = 45°
Incorrect
Explanation: ∠AOC = ∠AOB + ∠BOC
So, ∠AOC = 60° + 30°
∴ ∠AOC = 90°
An angle subtended by an arc at the centre of the circle is twice the angle subtended by that arc at any point on the rest part of the circle.
So,
∠ADC = 1/2∠AOC
= 1/2 × 90° = 45°
Question 10 of 10
10. Question
In the given figure, find angle OPR.
Correct
Explanation: The angle subtended by an arc at the centre of the circle is twice the angle subtended by that arc at any point on the circle.
So, ∠POR = 2 × ∠PQR
We know the values of angle PQR as 100°
So, ∠POR = 2 × 100° = 200°
∴ ∠POR = 360° – 200° = 160°
Now, in ΔOPR,
OP and OR are the radii of the circle
So, OP = OR
Also, ∠OPR = ∠ORP
By angle sum property of triangle, we knwo:
∠POR + ∠OPR + ∠ORP = 180°
∠OPR + ∠OPR = 180° – 160°
As, ∠OPR = ∠ORP
2∠OPR = 20°
Thus, ∠OPR = 10°
Incorrect
Explanation: The angle subtended by an arc at the centre of the circle is twice the angle subtended by that arc at any point on the circle.
So, ∠POR = 2 × ∠PQR
We know the values of angle PQR as 100°
So, ∠POR = 2 × 100° = 200°
∴ ∠POR = 360° – 200° = 160°
Now, in ΔOPR,
OP and OR are the radii of the circle
So, OP = OR
Also, ∠OPR = ∠ORP
By angle sum property of triangle, we knwo:
∠POR + ∠OPR + ∠ORP = 180°
∠OPR + ∠OPR = 180° – 160°
As, ∠OPR = ∠ORP
2∠OPR = 20°
Thus, ∠OPR = 10°