Introduction to Circles

Q. Question 1
The radii of two circles are 19 cm and 9 cm respectively. Find the radius of the circle which has circumference equal to the sum of the circumferences of the two circles.

Q. Line joining point of contact of tangent to centre of circle is perpendicular to ________ .

1. radius
2. secant
3. tangent
4. diameter

Q. Identify the minor segment in the given image.
(O is the centre of the circle)

1. 
2. 
3. 

Q. Sector is the region between a chord and its corresponding arc.

1. False
2. True

Q. Three circles touch each other externally. The distance between their centres is 5 cm, 6 cm and 7 cm. Find the radii of the circles.

1. 1 cm, 2.5 cm, 3.5 cm
2. 1 cm, 2 cm, 4 cm
3. 2 cm, 3 cm, 4 cm
4. 3 cm, 4 cm, 1 cm

Q.

What is a sector?

1. The portion of the circular region enclosed by two radii and the corresponding arc

2. The portion of circular region enclosed between a chord and the corresponding arc

3. The portion of circular region enclosed inside boundary of circle

4. The portion of circular region enclosed inside boundary of circumference

Q. Two equal sides of an isosceles triangle are given by $7x-y+3=0$ and $x+y-3=0$ and the third side passes through the point $(1,10),$ the slope $m$ of the third side is given by

1. $3m^2-1=0$
2. $m^2+1=0$
3. $3m^2+8m-3=0$
4. $m^2-3=0$

Q. The number of tangents, that can be drawn to a circle, parallel to a given secant is ______.

1. 0
2. 1
3. 2
4. None of these

Q.

The circumference of a circular field is 528 cm. Then its radius is __________.

1. 42 cm

2. 84 cm

3. 72 cm

4. 56 cm

Q. If the radius of a circle passing through all vertices of a rectangle is 4cm. Find the length of its diagonal.

1. 8

Q. If $\angle BOC=80°$and OA bisects $\angle BAC$, then find the value of $\angle ABO$ in degrees.

1. 20

Q. A chord divides a circle into major and minor _____.

1. Segment
2. Sector
3. Radius
4. Arc

Q. How many tangents can be drawn from a point inside the circle?

Q. Solve:$15x^2-64x+64=0$.

Q. The length of the tangent from an external point A on a circle with centre O is:

1. equal to OA
2. cannot be estimated
3. always greater than OA
4. always less than OA

Q. Mark the correct option.
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 : The length of the tangents drawn from an external point to a circle are equal.

1. Assertion (A) is false, but reason (R) is true.
2. Assertion (A) is true, but reason (R) is false.
3. Both assertion (A) and reason (R) are true, and reason (R) is the
   correct explanation of assertion (A).
4. Both assertion (A) and reason (R) are true, but reason (R) is not the correct explanation of assertion (A).

Q. Label the parts marked in the following circle.

1. Chord
2. Radius
3. Diameter

Q. Label the parts marked in the following circle.

1. Diameter
2. Radius
3. Chord