## Important Questions for Class 10 Maths Circles

1. AOB is a diameter of a circle with centre O and AC is a tangent to the circle at A. If

130°, then find angle ACO

a) 40^{0} b) 60^{0} c) 90^{0} d) 80^{0}

2. If the angle between two radii of a circle is 130^{0}, then the angle between the tangents at the end is _____

a) 50^{0} b) 60^{0} c) 70^{0} d) 80^{0}

3. If radii of two concentric circles are 4 cm and 5 cm, then the length of each chord of one circle which is tangent to the other circle is

a) 3 cm b) 6 cm c) 9 cm d) 1 cm

4. If angle between two tangents drawn from a point P to a circle of radius a and centre O is 60^{0}, then OP = ___

a) 2a b) a√3 c) a√2 d) 3a

5.A quadrilateral ABCD is drawn to circumscribe a circle. If AB = 12cm, BC = 15 cm and CD = 14 cm, then AD = ____

a) 11 cm b) 12 cm c) 13 cm d) 14 cm

**SUBJECTIVE QUESTIONS**

6. If the angle between two tangents drawn from an external point P to circle of radius ‘a’ and centre ‘O’ is 60^{0}, then find the length OP.

7. A circle is inscribed in a ΔABC, such that it touches the sides AB, BC and CA at points D, E and F respectively. If the lengths of sides AB, BC and CA are 12 cm, 8 cm and 10 cm respectively, find the lengths of AD, BE and CF

8. The incircle of

AF + BD + CE = AE + BF + CD = 1/2 (Perimeter of ∆𝐴𝐵𝐶)

9. In figure, the chord AB of the larger of the two concentric circles, with centre O, touches the smaller circle at C. Prove that AC = CB.

10..In figure, CP and CQ are tangents from an external point C to a circle with centre O. AB is another tangent which touches the circle at R. If CP = 11 cm and BR = 4 cm, find the length of BC.

11. Two tangents RQ and RP are drawn from an external point R to a circle with centre O. If PRQ = 120^{0}, then prove that OR = PR + RQ.

**12. Assertion:** If length of a tangent from an external point to a circle is 8 cm, then length of the other tangent from the same point is 8 cm.**Reason:** Length of the tangents drawn from an external point to a circle are equal.

13.**CASE STUDY**: A Ferris wheel (or a big wheel in the United Kingdom) is an amusement ride consisting of a rotating upright wheel with multiple passenger-carrying components (commonly referred to as passenger cars, cabins, tubs, capsules, gondolas, or pods) attached to the rim in such a way that as the wheel turns, they are kept upright, usually by gravity. After taking a ride in Ferris wheel, Aarti came out from the crowd and was observing her friends who were enjoying the ride . She was curious about the different angles and measures that the wheel will form. She forms the figure as given below.

In the given figure

1. Find angle ROQ

2. Find angle RQP

3. Find angle RSQ

4. Find angle ORP

Ncert Solutions Class 10 Maths Exercise 1.1 https://10thmathsguide.com/exercise-11-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 1.2

Ncert Solutions Class 10 Maths Exercise 2.1 https://10thmathsguide.com/exercise-21-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 2.2

Ncert Solutions Class 10 Maths Exercise 3.1 https://10thmathsguide.com/exercise-31-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.2 https://10thmathsguide.com/exercise-32-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 3.3 https://10thmathsguide.com/exercise-33-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.1 https://10thmathsguide.com/exercise-41-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.2 https://10thmathsguide.com/exercise-42-class-10-maths/

Ncert Solutions Class 10 Maths Exercise 4.3 https://10thmathsguide.com/exercise-43-class-10-maths/

MCQ VIDEOS ALL CHAPTERS CLASS 10 MATHShttps://www.youtube.com/watch?v=-eBlHyBxjLg&list=PL2uPMjJCHErQZZNipbsnagBqPrCU_WRN8

**MCQ Questions for Class 10 Maths all Chapters****https://sharmatutorial.in/category/mcq-class-10-maths/**