Diameter

Q.

The radius of a circle is $13$ cm and the length of one of its chords is $10$ cm. Find the shortest distance of the chord from the centre.

1. $13$ cm

2. $14$ cm

3. $11$ cm

4. $12$ cm

Q.

What will be the diameter of a circle whose radius is 15 cm?

1. 10 cm

2. 30 cm

3. 45 cm

4. 15 cm

Q.

Let C be the mid-point of an arc AB of a circle such that m$\stackrel{⌢}{AB}={183}^o$. If the region bounded by the arc ACB and line segment AB is denoted by S, then the centre O of the circle lies

1. on the segment AB

2. in the exterior of S

3. in the interior of S

4. on AB and bisects AB

Q.

Find the diameter of a circle if the radius is:

$3cm$

Q.

Find the diameter of a circle if the radius is:

$9cm$

Q. The length of a chord which is at a distance of 12cm from the centre of a circle of radius 3cm is

Q.

A road $3.5m$ wide surrounds a circular plot whose circumference is $44m.$ find the cost of paving the road at $Rs.50$ per $m^2.$

Q.

If two diameters of a circle intersect each other at right angles, then quadrilateral formed by joining their end points is a

1. rectangle

2. square

3. parallelogram

4. rhombus

Q. In a circle, the major arc is 3 times the minor arc. The corresponding central angles and the degree measures of two arcs are

(a) 90° and 270°

(b) 90° and 90°

(c) 270° and 90°

(d) 60° and 210°

Q.

One chord of a circle is known to be $10cm.$ The radius of this circle must be

1. greater than $5cm$

2. $5cm$

3. greater than or equal to $5cm$

4. less than $5cm$

Q.

AD is a diameter of a circle and AB is a chord. If AD = 34 cm and AB = 30 cm, the distance of AB from the centre of the circle is :

1. 8 cm

2. 4 cm

3. 15 cm

4. 17 cm

Q. The measure of angle subtended by a diameter in a semicircle is

1. 
   ${60}^{\circ }$
2. 
   ${90}^{\circ }$
3. 
   ${45}^{\circ }$
4. 
   ${180}^{\circ }$

Q.

The greatest chord of a circle is called its

1. radius

2. secant

3. diameter

4. none of these

Q.

The diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm is

1. 62 cm

2. 31 cm

3. 50 cm

4. 25 cm

Q.

Draw any circle and mark: its center , a radius , a diameter , a sector , a segment , a point in its interior, a point in its exterior and an arc.

Q.

If the circumference of a circular sheet is $154$ m. Find its radius. Also find the area of the sheet.

Q.

In the figure, AB and AC are two equal chords of a circle of radius 5 cm. If AB = AC = 6 cm, find the length of chord BC.

1. 9.6 cm

2. 10.6 cm

3. 8.6 cm

4. 7.6 cm

Q.

The figure shows that O is the centre of the circle and XOY is a diameter. If XZ is any other chord of the circle, then

1. XY > XZ

2. XY < XZ

3. XY = OZ

4. XY = XZ

Q.

Prove that the line segment joining the mid-point of the hypotenuse of a right triangle to its opposite vertex is half of the hypotenuse.

Q.

A circle of radius 26 cm has a chord of length 20 cm, then the distance of the chord from the centre is

1. 30 cm

2. 12 cm

3. 24 cm

4. 40 cm

Q.

If the radius of the circle is $4.5cm$, find the diameter of the circle.

Q.

Assertion: Two diameters of a circle intersect each other at right angles. Then the quadrilateral formed by joining their end-points is a square.

Reason: Angle in a semi-circle is a right angle.

Which of the following options is correct?

1. Assertion is true, but the reason is false.

2. Assertion is false, but the reason is true.

3. Both assertion and reason are true and reason is the correct explanation of assertion.

4. Both assertion and reason are true, but reason is not the correct explanation of assertion.

Q. Question 1 (iii)
Fill in the blanks:

(iii) The longest chord of a circle is the __________ of the circle.

Q.

In the given figure O is the centre of circle. If ∠OAB = 30^o and ∠OCB = 40^o, then measure of ∠AOC is :

1. 220^o

2. 70^o

3. 140^o

4. 110^o

Q.

_________ is the point of intersection of two diameters.

Q.

Find the radius of circle where diameter of circle is $11cm$$?$

Q.

In a circle, the length of an arc of central angle 40° is 3 centimetres. What is the perimeter of the circle? What is its radius?

Q. The longest chord of a circle is called

1. 
   Chord
2. 
   Radius
3. 
   Diameter
4. 
   Circumference

Q. 24. A circle centered at P woth radius 4 cm and another circle centered at Q with radius 16 cm touch each otger externally. A third circle woth centre R is drawn to touch the first two circle and one of their common tangent. Then the radius of the cirle R is

Q. In the given figure, O is the centre of a circle and ∠ACB = 30°. Then, ∠AOB = ?
(a) 30°
(b) 15°
(c) 60°
(d) 90°
Figure