Home / Class 10 Math / Ch 10 Circles- MCQ Online Test 2 Class 10 Maths
Chapter 10 Circles- MCQ Online Test 2 Class 10 Maths
1.The length of tangent PQ, from an external point P is 24 cm. If the distance of the point P from the centre is 25 cm, then the diameter of the circle is
14 cm. 17 cm. 12 cm. 19 cm.
2. A tangent PQ at point of contact P to a circle of radius 12 cm meets the line through centre O to a point Q such that OQ = 20 cm, length of tangent PQ is :
16 cm 12 cm 19 cm 11 cm
3. PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such ∠POR = 120∘, then ∠OPQ is 50° 30° 80° 35°
4. A circle is inscribed in ΔABC having sides 8 cm, 10 cm and 12 cm as shown in the figure. Then
AD = 7 cm, BE = 4 cm. AD = 7 cm, BE = 5 cm. AD = 8 cm, BE = 5 cm. AD = 10 cm, BE = 5 cm.
5. In the given figure, If TP and TQ are two tangents to a circle with centre O, so that ∠POQ = 110o then ∠PTQ is equal to
20° 40° 70° 90°
6. A tangent PQ at a point P o a circle of radius 5 cm meets a line through the centre O at point Q, so that OQ = 12 cm. find the length PQ.
16 cm. 30 cm. 26 cm. 22 cm.
7. From a point Q, the length of tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm, radius of circle is :
11 cm 7 cm 9 cm 10 cm
8. If PA and PB are tangents to the circle with centre O such that ∠APB = 40∘, then ∠OAB is equal to
40° 80° 20° 70°
9. Quadrilateral PQRS circumscribes a circle as shown in the figure. The side of the quadrilateral which is equal to PD + QB is
PR QR PQ RS
10. In the given figure, the pair of tangents A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm, then the radius of the circle is :
3 cm 4 cm 5 cm 2.5 cm
Class 10 Circles Quiz -2
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Question 1 of 10
1. Question
The length of tangent PQ, from an external point P is 24 cm. If the distance of the point P from the centre is 25 cm, then the diameter of the circle is
Correct
Here ∠OPQ = 90°[Angle between tangent and radius through the point of contact]
∴ OQ2 = OP2 + PQ2
= (25)2 = OP2 + (24)2
⇒ OP2 = 625 – 576
⇒ OP2 = 49
⇒ OP = 7 cm
Therefore, the diameter = 2 x OP = 2 x 7 = 14 cm
Incorrect
Here ∠OPQ = 90°[Angle between tangent and radius through the point of contact]
∴ OQ2 = OP2 + PQ2
= (25)2 = OP2 + (24)2
⇒ OP2 = 625 – 576
⇒ OP2 = 49
⇒ OP = 7 cm
Therefore, the diameter = 2 x OP = 2 x 7 = 14 cm
Question 2 of 10
2. Question
A tangent PQ at point of contact P to a circle of radius 12 cm meets the line through centre O to a point Q such that OQ = 20 cm, length of tangent PQ is :
Correct
Since op is perpendicular to PQ, the ∠OPQ = 90°
Now, in right angled triangle OPQ,
Incorrect
Since op is perpendicular to PQ, the ∠OPQ = 90°
Now, in right angled triangle OPQ,
Question 3 of 10
3. Question
PQ is a tangent drawn from a point P to a circle with centre O and QOR is a diameter of the circle such ∠POR = 120∘, then ∠OPQ is
Correct
Incorrect
Question 4 of 10
4. Question
A circle is inscribed in ΔABC having sides 8 cm, 10 cm and 12 cm as shown in the figure. Then
Correct
Let AD = x and BE = y
∴ BD = 12 – x ⇒ BE = 12 – x [BD = BE = Tangents to a circle from an external point]
⇒ y = 12 – x ⇒ x+y = 12…….(i)
Also, AF = x and CF = 10 – x and CE = 8 – y
Also, AF = x and CF = 10 — x and CE = 8 – y
∴ 10 – x = 8 – yx – y = 2 (ii)
On solving eq. (i) and (ii), we get x = 7 and y = 5
⇒ AD = 7 cm and BE = 5cm
Incorrect
Let AD = x and BE = y
∴ BD = 12 – x ⇒ BE = 12 – x [BD = BE = Tangents to a circle from an external point]
⇒ y = 12 – x ⇒ x+y = 12…….(i)
Also, AF = x and CF = 10 – x and CE = 8 – y
Also, AF = x and CF = 10 — x and CE = 8 – y
∴ 10 – x = 8 – yx – y = 2 (ii)
On solving eq. (i) and (ii), we get x = 7 and y = 5
⇒ AD = 7 cm and BE = 5cm
Question 5 of 10
5. Question
In the given figure, If TP and TQ are two tangents to a circle with centre O, so that ∠POQ = 110o then ∠PTQ is equal to
Correct
Since the angle between the two tangents drawn from an external point to a circle in supplementary of the angle between the radii of the circle through the point of contact.
∴ ∠PTQ = 180∘−110∘ = 70∘
Incorrect
Since the angle between the two tangents drawn from an external point to a circle in supplementary of the angle between the radii of the circle through the point of contact.
∴ ∠PTQ = 180∘−110∘ = 70∘
Question 6 of 10
6. Question
A tangent PQ at a point P o a circle of radius 5 cm meets a line through the centre O at point Q, so that OQ = 12 cm. find the length PQ.
Correct
Incorrect
Question 7 of 10
7. Question
From a point Q, the length of tangent to a circle is 24 cm and the distance of Q from the centre is 25 cm, radius of circle is :
Correct
Here ∠OPQ = 90° [Tangent makes right angle with the radius at the point of contact]
∴ OQ2 = OP2 + PQ2
= (25)2 = OP2 + (24)2
⇒ OP2 = 676 – 576 = 49
⇒ OP = 7 cm
Therefore, the radius of the circle is 7 cm
Incorrect
Here ∠OPQ = 90° [Tangent makes right angle with the radius at the point of contact]
∴ OQ2 = OP2 + PQ2
= (25)2 = OP2 + (24)2
⇒ OP2 = 676 – 576 = 49
⇒ OP = 7 cm
Therefore, the radius of the circle is 7 cm
Question 8 of 10
8. Question
If PA and PB are tangents to the circle with centre O such that ∠APB = 40∘, then ∠OAB is equal to
Correct
Let ∠OAB = ∠OBA = x [Opposite angles of opposite equal radii] And ∠AOB =180° – 40° = 140°
Now, in triangle AOB,
∠OAB + ∠OBA + ∠AOB = 180°
⇒ x + x +140° = 180°
⇒ 2x = 40°
⇒ x = 20°
∴ ∠OAB = 20°
Incorrect
Let ∠OAB = ∠OBA = x [Opposite angles of opposite equal radii] And ∠AOB =180° – 40° = 140°
Now, in triangle AOB,
∠OAB + ∠OBA + ∠AOB = 180°
⇒ x + x +140° = 180°
⇒ 2x = 40°
⇒ x = 20°
∴ ∠OAB = 20°
Question 9 of 10
9. Question
Quadrilateral PQRS circumscribes a circle as shown in the figure. The side of the quadrilateral which is equal to PD + QB is
Correct
PD + QB = PA + QA [Tangents from an external point to a circle are equal]
⇒PD + QB = PQ
Incorrect
PD + QB = PA + QA [Tangents from an external point to a circle are equal]
⇒PD + QB = PQ
Question 10 of 10
10. Question
In the given figure, the pair of tangents A to a circle with centre O are perpendicular to each other and length of each tangent is 5 cm, then the radius of the circle is :
Correct
Tangents AP = AQ
In △APO and △AQO,
AP = AQ
AO is Common
OP = OQ
Thus, △APO ~ △AQO
Now as we know, the angle in a semicircle is 90°.
Thus,
∠P = ∠Q = ∠O =90°
Thus, we can say that OP = OQ = AP = AQ
Thus the radius of the circle is 5 cm.
Incorrect
Tangents AP = AQ
In △APO and △AQO,
AP = AQ
AO is Common
OP = OQ
Thus, △APO ~ △AQO
Now as we know, the angle in a semicircle is 90°.
Thus,
∠P = ∠Q = ∠O =90°
Thus, we can say that OP = OQ = AP = AQ
Thus the radius of the circle is 5 cm.
