Circles cbse 10 board exam triangles and circles

It gives you detail expression about circle

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| shimon_ joseph Circles| CBSE| Class 10| L1| Problem solving |Asaltu

4. In the following figure, AT is a tangent to the circle with centre O such that OT =
4 cm and ∠OTA = 30°. Then AT is equal to
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
2√3cm
2 cm
2√2 cm
√3cm

5. In the following figure, AT is a tangent to the circle with centre O such that OT =
4 cm and ∠OTA = 30°. Then AT is equal to
CBSE 2023
D
C
A
B
2√3cm
2 cm
2√2 cm
√3cm
Mathematics | CBSE - Class 10 | Circles | Important PYQs

6. From an external point, two tangents are drawn to a circle. Prove that the line
joining the external point to the centre of the circle bisects the angle between
the two tangents.
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
O
P
A
B

7. Two concentric circles are of radii 4 cm and 3 cm. Find the length of the chord of
the larger circle which touches the smaller circle.
CBSE 2022
Mathematics | CBSE - Class 10 | Circles | Important PYQs
O
4
3
P
A
Q
∟

8. Two concentric circles are of radii 5 cm and 3 cm. Find the length of
the chord of the larger circle which touches the smaller circle.
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
O
3
AP Q4
5
∟

9. In figure, a quadrilateral ABCD is drawn to circumscribe a circle. Prove that AB +
CD = BC + AD.
CBSE 2020( 2 marks)
Mathematics | CBSE - Class 10 | Circles | Important PYQs
A
D
B
C

10. In figure, find the perimeter of ⃤ ABC, if AP = 12cm.
CBSE 2020( 2 Marks)
Mathematics | CBSE - Class 10 | Circles | Important PYQs

11. In the figure below, a triangle ABC with B = 90º is shown. Taking AB as diameter,
a circle has been drawn intersecting AC at point P. Prove that the tangent
drawn at point P bisects BC.
CBSE 2022
Mathematics | CBSE - Class 10 | Circles | Important PYQs

12. Draw a circle of radius 3 cm. Take two points P and Q on one of its extended
diameter each at a distance of 7 cm from its centre. Construct tangents to the
circle from these two points P and Q.
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Mathematics | CBSE - Class 10 | Circles | Important PYQs

13. In Fig. , AB is diameter of a circle centered at O. BC is a tangent to the circle at B.
If OP bisects the chord AD and ∠AOP = 60° then find m∠C .
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Mathematics | CBSE - Class 10 | Circles | Important PYQs

14. In Fig. 2, XAY is a tangent to the circle centred at O. If ∠ABO = 40°, then find m
∠BAY and m ∠AOB.
CBSE 2022
Mathematics | CBSE - Class 10 | Circles | Important PYQs

15. In Fig. 4, PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P
and Q meet at a point T. Find the length of TP.
CBSE 2022
Mathematics | CBSE - Class 10 | Circles | Important PYQs

16. In the given figure, PQ is a tangent to the circle with centre O. If ∠ OPQ = x,
∠POQ = y , then x + y is
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
45°
90°
60°
180°

17. In the given figure, PQ is a tangent to the circle with centre O. If ∠ OPQ = x,
∠POQ = y , then x + y is
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
45°
90°
60°
180°

18. In Figure 2, PQ and PR are tangents to the circle centred at O. If ∠OPR = 45° ,
then prove that ORPQ is a square.
CBSE 2022
Mathematics | CBSE - Class 10 | Circles | Important PYQs

19. A chord of a circle of radius 14 cm subtends an angle of 60° at the centre. Find
the area of the corresponding minor segment of the circle. Also find the area of
the major segment of the circle.
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Mathematics | CBSE - Class 10 | Circles | Important PYQs

20. In the given figure, PA and PB are tangents from external point P to a circle with
centre C and Q is any point on the circle. Then the measure of ∠AQB is
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
62(½)°
125°
55°
90°

21. In the given figure, PA and PB are tangents from external point P to a circle with
centre C and Q is any point on the circle. Then the measure of ∠AQB is
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
62(½)°
125°
55°
90°

22. In the given figure, O is the centre of the circle. AB and AC are tangents drawn to
the circle from point A. If ∠BAC = 65° , then find the measure of ∠BOC .
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs

23. In the given figure, AB is a tangent to the circle centered at O. If OA = 6 cm and
∠OAB = 30°, then the radius of the circle is :
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
2 cm
3 cm
3√3 cm
√3 cm

24. In the given figure, AB is a tangent to the circle centered at O. If OA = 6 cm and
∠OAB = 30°, then the radius of the circle is :
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
2 cm
3 cm
3√3 cm
√3 cm

25. Two tangents TP and TQ are drawn to a circle with centre O from an external
point T. Prove that ∠PTQ = 2∠OPQ .
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Mathematics | CBSE - Class 10 | Circles | Important PYQs

26. A circle touches the side BC of a ABC at a point P and touches AB and AC when
produced at Q and R respectively. Show that AQ = ½ (Perimeter of ⃤ ABC ).
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Mathematics | CBSE - Class 10 | Circles | Important PYQs

27. In the figure, TP and TQ are tangents drawn to the circle with centre at O. If
∠POQ = 115° then ∠PTQ is :
CBSE 2020
D
C
A
B
115°
57.5°
55°
65°
Mathematics | CBSE - Class 10 | Circles | Important PYQs

28. In the figure, TP and TQ are tangents drawn to the circle with centre at O. If
∠POQ = 115° then ∠PTQ is :
CBSE 2020
D
C
A
B
115°
57.5°
55°
65°
Mathematics | CBSE - Class 10 | Circles | Important PYQs

29. In the given figure, PA is tangent to the circle drawn from the external point P
and PBC is the secant to the circle with BC as diameter. If ∠AOC = 130° , then
find the measure of APB , where O is the centre of the circle.
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Mathematics | CBSE - Class 10 | Circles | Important PYQs

30. Two circles with centres O and O of radii 6 cm and 8 cm, respectively intersect
at two points P and Q such that OP and O’P are tangents to the two circles. Find
the length of the common chord PQ.
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs

31. Prove that the angle between the two tangents drawn from an external point to
a circle is supplementary to the angle subtended by the line-segment joining
the points of contact at the centre.
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs

32. If two tangents are inclined at 60˚ are drawn to a circle of radius 3cm then find
length of each tangent.
CBSE 2021
D
C
A
B
3√3/2 cm
6 cm
3 cm
3√3 cm
Mathematics | CBSE - Class 10 | Circles | Important PYQs

33. If two tangents are inclined at 60˚ are drawn to a circle of radius 3cm then find
length of each tangent.
CBSE 2021
D
C
A
B
3√3/2 cm
6 cm
3 cm
3√3 cm
Mathematics | CBSE - Class 10 | Circles | Important PYQs

34. The discus throw is an event in which an athlete attempts to throw a discus. The athlete
spins anti-clockwise around one and half times through a circle, then releases the throw.
When released, the discus travels along tangent to the circular spin orbit.

In the given figure, AB is one such tangent to a circle of radius 75 cm. Point O is centre of the
circle and . ∠ABO = 30°. PQ is parallel to OA.
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
Based on the above information:
(a) find the length of AB.
(b) find the length of OB.
(c) find the length of AP.

35. In the given figure, a circle is inscribed in a quadrilateral ABCD in which
∠B = 90° . If AD= 17 cm AB = 20 cm and DS = 3 cm , then find the radius of the
circle.
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs

36. In the given figure, PQ is tangent to the circle centered at O. If ∠AOB = 95°,
then the measure of ∠ABQ will be
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
47.5°
42.5°
85°
95°

37. In the given figure, PQ is tangent to the circle centered at O. If ∠AOB = 95°,
then the measure of ∠ABQ will be
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
47.5°
42.5°
85°
95°

38. In the figure, PA and PB are two tangents to the circle with centre O such that
∠ APB = 50° . Then, the measure of ∠OAB is :
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
25°
50°
75°
100°

39. In the figure, PA and PB are two tangents to the circle with centre O such that
∠ APB = 50° . Then, the measure of ∠OAB is :
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs
D
C
A
B
25°
50°
75°
100°

40. If a hexagon ABCDEF circumscribes a circle, show that AB + CD + EF = BC + DE +
FA.
CBSE 2023
Mathematics | CBSE - Class 10 | Circles | Important PYQs

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