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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CBSE+NCERT+10th- Math-Chapter-10-Circles-test-paper

1. Prove that the parallelogram circumscribing a circle is rhombus.

Ans Given : ABCD is a parallelogram circumscribing a circle.

To prove : - ABCD is a rhombus

or

AB=BC=CD=DA

Proof: Since the length of tangents from external are equal in length

AS = AR …..(1)

BQ = BR …..(2)

QC = PC …..(3)

SD = DP …..(4)

Adding (1), (2), (3) & (4).

AS + SD + BQ + QC = AR + BR + PC + DP

AD + BC = AB + DC

AD + AD = AB + AB

Since BC = AD & DC = AB (opposite sides of a parallelogram are equal)

2AD = 2AB

AD = AB …..(5)

BC = AD (opposite sides of a parallelogram)

DC = AB …..(6)

From (5) and (6)

AB = BC = CD = DA

2. A circle touches the side BC of a triangle ABC at P and touches AB and AC when

produced at Q and R respectively as shown in figure. Show that AQ= 1/2(perimeter of triangle ABC)

3. XP and XQ are tangents from X to the circle with centre O. R is a point on the circle. Prove that XA+AR=XB+BR

4.  In figure, the incircle of triangle ABC touches the sides BC, CA, and AB at D, E, and F respectively. Show that AF+BD+CE=AE+BF+CD= 1/2(perimeter of triangle ABC),

5. 5. A circle touches the sides of a quadrilateral ABCD at P, Q, R and S respectively. Show that the angles subtended at the centre by a pair of opposite sides are supplementary.

Download full paper : 10th chapter-9 circles test paper Solved

CBSE TEST PAPER MATHEMATICS(Class-10)Circle

I. Fill in the blanks.
a. The word ‘tangent’ comes from the Latin word ------------ 
b. A tangent to a circle intersects it in ----------- point (s).
c. A line intersecting a circle in two points is called a --------
d. A circle can have -----------parallel tangents at the most.
e. The common point of a tangent to a circle and the circle is called ----------


2. Solve these questions (any five) 4X5=20

1. Prove that The tangent at any point of a circle is perpendicular to the radius through the point of contact

2. Prove that the lengths of tangents drawn from an external point to a circle are equal.

3. Two tangents TP and TQ are drawn to a circle with centre O from an external point T.(see fig. 1) Prove that < PTQ = 2 < OPQ.

4. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see Fig. 2) Find the length TP. 




4. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see Fig. 2) Find the length TP. 

4. PQ is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T (see Fig. 2) Find the length TP.

5. Prove that opposite sides of a quadrilateral circumscribing a circle subtend supplementary angles at the centre of the circle.




6. 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.

7. The length of a tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. Find the radius of the circle.

8. A triangle PQR is drawn to circumscribe a circle of radius 4cm. The circle touches QR at D such that   QD = 6 cm and RD = 8 cm. Find PQ and PR.

9. The tangent at a point C of a circle and a diameter AB when extended intersect at P. If <PCA = 110⁰ , find < CBA.


10. In the figure. X.Y. are two parallel tangents to a circle with Center O and another tangent AB with point of contact C intersecting XY at A and X.Y. at B. Prove that <AOB = 90⁰.
10th Maths SA-2 Chapter wise Test Papers Links

10th Maths SA-2 Chapter wise Test Papers Links
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