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Circles

Theory and Formula



Question


Q1. ABC is a right triangle right - angled at B such that BC = 6 cm and AB = 8 cm . find the radius of its circle.

(a) 8 cm (b) 2 cm (c) 4 cm (d) 10 cm

Solution.


r = (AB + BC + AC)/2

r = (8 + 6 - 10)/2

= 4/2

r = 2
Solution

Q2. If two circles touch internally, then the distances between their centers is equal to the difference of their radius.

(a) True (b) False (c) Can't say

Solution.
(a) True
Solution

Q3. The area of a square is 121 cm2. If the same wire is bent in the form of circle, find the area of the circle.

(a) 170 cm2 (b) 164 cm2 (c) 154 cm2 (d) 180 cm2

Solution.
Side of a square is 11,
So perimeter of square is 44
2πr = 44
2 x 22/7 x r = 44
r = 7 cm
Area of the circle = πr2 = 154
Solution

Q4. Find the circumference of a circle if radius is 2 cm.

(a) 4π (b) 6π (c) π (d) 3π

Solution.
(a) 4π
Solution

Q5. What is the area of a quadrant of a circle of radius 4r.

(a) 3πr2 (b) r2 (c) 4π (d) 4πr2

Solution.
Area of circle = πr2
= π(4r2) = 16πr2
Area of a quadrant = 16πr2/4
= 4πr2
Solution

Q6. (i) Circles having the same centre are called concentric circles.
(ii) The circles having same radii are congruent.
which statement is right .

(a) only (i) (b) only (ii) (c) both (d) none of these

Solution.
(c) both
Solution

Q7. How many circles passing through three non-collinear points.

(a) four (b) three (c) two (d) one

Solution.
(d) one
Solution

Q8. Angle in a semicircle is a __________ angle.

(a) 500 (b) 600 (c) 750 (d) 900

Solution.
(d) 900
Solution

Q9. Find the area of a circle if its diameter is √2 .

(a) 2π (b) π/2 (c) 2 (d) π

Answer.
(b) π/2
Solution

Q10. If two circles touch externally, then the distance between their centres is equal to the sum of their radii.

(a) True (b) False (c) Can't say

Solution.
(a) True
Solution