X Chapter Tangent of Circle BY JSUNIL TUTORIAL Questions Bank

X Chapter Tangent of Circle BY JSUNIL TUTORIAL Questions Bank for CBSE EXAMS

( 1 Mark Questions ) 

1. If radii of the two concentric circles are 15cm and 17cm , then find the length of each chord of one circle which is tangent to one other. Ans. 16cm

2. If two tangents making an angle of 120⁰  with each other , are drawn to a circle of radius 6cm, then find the angle between the two radii, which are drawn to the tangents.           Ans. 600

3. PQ is a chord of a circle and R is point on the minor arc. If PT is a tangent at point P such that 

< QPT = 60 then find <PRQ.                                 Ans. 1200 

4. If a tangent PQ at a point P of a circle of radius 5cm meets a line through the centre O at a point Q such that OQ = 12 cm then find the length of PQ.                           Ans. √119cm 

5. From a point P, two tangents PA and PB are drawn to a circle C(O,r) . If OP =2r ,then what is the type of APB.                                                   Ans. Equilateral triangle

6. If the angle between two radii of a circle is 130,then find the angle between the tangents at the end of the radii. Ans. 500. 

7. ABCD is a quadrilateral. A circle centred at O is inscribed in the quadrilateral. If AB = 7cm , BC = 4cm , CD = 5cm then find DA.   '                        Ans. 8 cm

8. In a triangle  ABC , AB = 8cm , <ABC = 90. Then find the radius of the circle inscribed in the triangle.            Ans. 2cm

( 2 Mark Questions ) 

9. Two tangents PA and PB are drawn from an external point P to a circle with centre O. Prove that OAPB is a cyclic quadrilateral. 

10. If PA and PB are two tangents drawn to a circle with centre O , from an external point P such that PA=5cm and < APB = 60, then find the length of the chord AB. Ans. 5cm

11.   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 and intersects PC and QC at A and B respectively . If CP = 11cm and BR = 4cm, then find the length of BC.              Ans. 7cm

12. If all the sides of a parallelogram touch a circle, show that the parallelogram is a rhombus.

13. Prove that the perpendicular at the point of contact to the tangent to a circle passes through the centre of the circle.

( Three Marks Questions) 

14. If quadrilateral ABCD is drawn to circumscribe a circle then prove that AB+CD=AD+BC.

15. Prove that the angle between the two tangents to a circle drawn from an external point, is supplementary to the angle subtended by the line segment joining the points of contact to the centre.

16. AB is a chord of length 9.6cm of a circle with centre O and radius 6cm. If the tangents at A and B intersect at point P then find the length PA. Ans. 8cm

17. The incircle of a ∆ABC touches the sides BC, CA &AB at D,E and F respectively. If AB=AC, prove that BD=CD.

18. Prove that the intercept of a tangent between two parallel tangents to a circle subtends a right angle at the centre of the circle

19. PQ and PR are two tangents drawn to a circle with centre O from an external point P. Prove that < QPR = 2< OQR.

( Four Marks Questions) 

20. Prove that the length of tangents drawn from an external point to a circle is equal. Hence, find BC, if a circle is inscribed in a ABC touching AB,BC &CA at P,Q &R respectively, having AB=10cm, AR=7cm &RC=5cm. Ans. 8cm

21. Prove that the tangent at any point of a circle is perpendicular to the radius through the point of contact. Using the above, do the following: If O is the centre of two concentric circles, AB is a chord of the larger circle touching the smaller circle at C, then prove that AC=BC.

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10th Chapter : Tangent of Circle Solved CBSE Test Paper
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Guess paper 10th Chapter_Arithmetic Progression

10th Math : Arithmetic Progression : Guess paper part-II

1.        Find the sum of 20 terms of the A.P. 1,4,7,10………

2.        If the nth terms of an A.P is (2n + 1), find the sum of first n terms of the A.P.

3.        Find the sum of first 30 terms of an A.P.whose second term is 2 and seventh term is 22.

4.        Find the sum of first 10 terms of an A.P., in which 3^rd term is 7 and 7^th term is two more than thrice of its 3^rd term.

5.        Find the sum of all even integers between 2 to 100 divisible by 2.

6.        Find the number of terms in the series 20, 19 1/3 + 18 2/3 +………of which the sum is 300,explain the double answer.

7.        If the mth term of an A.P. is 1/n and the nth terms is 1/m, show that the sum of mn terms is ½(nm + 1).

8.        If the sum of n terms of an A.P.is same as the sum of its n terms, show that the sum of its (m + n) terms is zero.

9.        Find the sum of first n odd natural numbers.

10.     If the 8^th terms of an A.P.is 31 and the 15^th terms is 16 more than the 11^th terms find the sum of first 20 terms.

11.     How many terms of A.P.: 24,21,18,…….. Must be taken so that their sum is 78?

12.     The angles of a triangle are in AP.If the greatest angle equals the sum of the other two, find the angles.

13.     Find the sum of two digits numbers, which are divisible by 7?

14.     Find the sum of number b/t 49 to 500 which are divisible by 7?

15.     If the p^th term of an A.P.is q and the q^th term is p, prove that its n^th term is (p + q – n) and find the sum of first (p+q)^th term .

16.      How many terms of the sequence 18,16,14…… should be taken so that their sum is zero.

17.     Write the first 5 terms of an AP whose nth term is given by (2n+1)/3.

18.     How many terms in the sequence -6  , -11/2 , -5 , -9/2 , …are needed to give the sum 0 ?

19.     Find the sum of all the natural numbers less than 100 which are divisible by 6.

20.     The sum of n terms of an A.P.; be 3n2 – n and its common difference is 6,find its first and 27^th term.

21.     The sum of nth terms of an A.P. is 3n²+ 5n, then find its nth term.

22.     Find the sum of first 21 terms Ö2 + Ö8 + Ö18 + Ö32………….

ARITHMETIC PROGRESSIONS MATHEMATICS CASS X- Guess paper part-II

                                                                                                 

1. How many two-digit numbers are divisible by 3?
2. Which term of A.P :3,8,13,18,…………………,is  78?
3. Check whether –150 is a term of the A.P 11,8,5,2………
4. If 3^rd and 9^th terms of an A.P are 4 and – 8 respectively, which term is 106.find the 29^th term?
5. The 8^th term of an AP is zero. Find the ratio of its 38^th term and 18th term.
6. Which term of A.P is 3,15,27,39……. will be 132 more then its 54^th terms?
7. Find the 20^th terms from the last terms of the A.P: 3,8,13,…………..253.
8. Determine the 15^th and 5^th term from the end of the A.P.: 4,9,14,…….,254.
9. Which term of A.P. :9,13,17,21,25……………………is 109.
10. If the 8^th terms of an A.P.is 31 and the 15^th terms is 16 more than the 11^th terms.
11. If 10^th term of an A.P is 52 and 17^th terms is 20 more than the 13^th terms find the A.P.
12. Determine the general terms of A.P. whose 7^th terms is – 1 and 16^th term 17.also find it’s 25^th term.
13. How many numbers of two digits are divisible by 7 ?
14. Find the number of integers b/t 49 to 500 which are divisible by 7?
15. If the p^th term of an A.P.is q and the q^th term is p, prove that its n^th term is (p + q – n ) and (p+q)^th term is zero.
16. If m times the m^th term of an A.P. is equal to n times the n^th term, show that the (m+n)^th terms of an A.P is zero.
17. The 4^th term of an A.P. is three times the first and 7^th term exceeds twice the third term by 1.find the A.P.
18. The sum of three numbers in A.P. is – 3 ,and their product is 8. Find the numbers.
19. If 2x,x + 10, 3x + 2 are in A.P., Find the value of x.
20. For what value of n ,the n^th terms of the arithmetic progressions 63,65,67……..and 3,10,17,…………are equal?

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