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) 400 b) 600 c) 900 d) 800
2. If the angle between two radii of a circle is 1300, then the angle between the tangents at the end is _____
a) 500 b) 600 c) 700 d) 800
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 600, 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 600, 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
![Important Questions for Class 10 Maths Circles](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16794762926465330378211214578609.jpg?resize=900%2C506&ssl=1)
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.
![Important Questions for Class 10 Maths Circles](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-1679539344600604072615022568555.jpg?resize=300%2C231&ssl=1)
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.
![Important Questions for Class 10 Maths Circles](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16795393445221633254596675743688.jpg?resize=300%2C153&ssl=1)
11. Two tangents RQ and RP are drawn from an external point R to a circle with centre O. If PRQ = 1200, 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.
![Important Questions for Class 10 Maths Circles](https://i0.wp.com/10thmathsguide.com/wp-content/uploads/2023/03/wp-16795393440494307461279428268193.jpg?resize=300%2C212&ssl=1)
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 Chaptershttps://sharmatutorial.in/category/mcq-class-10-maths/