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

ASSIGNMENT AREAS RELATED TO CIRCLES CLASS X

AREAS RELATED TO CIRCLES CLASS X
1. The radius of the circle is 3 m. What is the circumference of another circle, whose area is 49 times that of the first?

2. Two circles touch externally. The sum of their areas is 130 p sq. cm and the distance between their centres is 14 cm. Find the radii of the circles.

3. A wire when bent in the form of an equilateral triangle encloses an area of 121 √3 cm² . If the same wire is bent in the form of a circle, find the area of the circle.

4. The area enclosed between the two concentric circles is 770 cm2. If the radius of the outer circle is 21 cm, calculate the radius of the inner circle.

5. A wheel of diameter 42 cm, makes 240 revolutions per minute. Find :

(i) the total distance covered by the wheel in one minute. (ii) the speed of the wheel in km/hr.

6. An arc of length 20pcm subtends an angle of 144° at the centre of the circle. Find radius of circle.

7. The perimeter of a sector of a circle of radius 5.7 m is 27.2 m. Find the area of the sector.

8. In the given figure, the length of the minor arc is 7/24 of the circumference of the circle. Find : 
(i) <AOB

(ii) If it is given that the circumference of the circle is 132 cm, find the length of the minor arc AB and the radius of the circle.

9. A chord of a circle of radius 10 cm subtends a right angle at the centre. Find :

(i) Area of the minor sector (ii) Area of the minor segment

(iii) Area of major sector (iv) Area of major segment ( use p = 3.14 )

10. A chord of a circle of radius 12 cm subtends an angle of 120° at the centre. Find the area of the corresponding segment of the circle. [use p = 3.14, √3 = 1.73]

11. In the given figure, ABC is an equilateral triangle inscribed in a circle of radius 4 cm. Find the area of the shaded region.

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12. The following figure shows a rectangle ABCD inscribed in a circle.

(i) If AB = 8 cm and BC = 6 cm, find the area of the circle not included in the rectangle.

(ii) If diameter of the circle is 25 cm and BC = 15 cm, find the area of the circle not included in the given rectangle.

13. A paper is in the form of a rectangle ABCD in which AB = 20 cm and BC = 14 cm. A semi circular portion with BC as diameter is cut off. Find the area of the remaining part 

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X Maths Comprehensive Test chapter Probability

X Maths Comprehensive Test chapter Probability
Q1. A lot consists of 144 ball pens of which 20 are defective and the others are good. Nuri will buy a pen if it is good, but will not buy if it defective. The shopkeeper draws one pen at random and gives it to her. What is the probability that

(i) She will buy it? (ii) She will not buy it?

Q2. An unbiased die is thrown. What is the probability of getting:
(i) an even number or a multiple of 3
(ii) an even number and multiple of 3
(iii) a number 3 or 4.

Q3. Two unbiased coins are tossed simultaneously. Find the probability of getting
(i) at least one head. (ii) at most one head. (iii) No head.

Q4. Three unbiased coins are tossed together. Find the probability of getting:
(i) all heads (ii) at least two heads

Q5. Two dice are thrown simultaneously. Find the probability of getting :
(i) the sum as a prime number
(ii) a total of at least 10
(iii) a doublet of even number
(iv) a multiple of 2 on one dice and a multiple of 3 on the other.

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