Chords and Their Distances from the Centre of the Circle

Q. A Circle of radius 25 units has a chord going through a point that is located 10 units for the center. What is the shortest possible length that chord could have?

1. $25units$
2. $\sqrt{525}units$
3. $40units$
4. $\sqrt{2100}units$

Q. In the given figure, OP and OQ are perpendicular bisectors of chords CD and AB respectively. If PD = 4 cm and OP = OQ = 3 cm, then what will be the length of chord AB?

1. 4 cm
2. 5 cm
3. 8 cm
4. 6 cm

Q. In the given figure, CD is a chord 3 cm away from the centre of the circle. What will be the length of CD if the radius of the circle is 5 cm?

1. 6 cm
2. 8 cm
3. 4 cm
4. 7 cm

Q. Question 1
AD is a diameter of a circle and AB is a chord. If AD = 34cm, AB = 30cm, the distance of AB from the centre of the circle is

(A) 17 cm
(B) 15 cm
(C) 4 cm
(D) 8 cm

Q.

In a circle of radius 13 cm, two chords MN and JK are at a
distance of 5 cm from the centre. Find the measure of (MN+2×JK).

Q. In the given figure, CD is a chord 3 cm away from the centre of the circle. What will be the length of CD if the radius of the circle is 5 cm?

1. 6 cm
2. 8 cm
3. 4 cm
4. 7 cm

Q. In the given figure, OP and OQ are perpendicular bisectors of chords CD and AB respectively. If PD = 4 cm and OP = OQ = 3 cm, then what will be the length of chord AB?

1. 4 cm
2. 5 cm
3. 8 cm
4. 6 cm

Q. In the given figure, OP and OQ are perpendicular bisectors of chords CD and AB respectively. If PD = 4 cm and OP = OQ = 3 cm, then what will be the length of chord AB?

1. 4 cm
2. 8 cm
3. 6 cm
4. 5 cm

Q. Equal chords of a circle are equidistant from the centre.

1. True
2. False

Q. Chords equidistant from the centre of a circle need not be equal in length.

1. True
2. False

Q. In the given figure, 𝑪𝑫 is a chord 𝟔 𝒄𝒎 away from the centre of the circle. What will be the length of 𝑪𝑫 if the radius of the circle is 𝟏𝟎 𝒄𝒎?

1. 14 cm
2. 16 cm
3. 12 cm
4. 8 cm

Q.

If AB is a chord which passes through the centre O of a circle, then what is AB known as?

1. Diameter of the circle

2. Radius of the circle

3. Sector of the circle

4. Segment of the circle

Q.

If the chord AB of a circle with centre O is the longest chord of the circle, then ∠AOB = _____.

1. 90${}^{\circ }$
2. 45${}^{\circ }$
   
3. 180${}^{\circ }$
4. 360${}^{\circ }$

Q. In the given figure, what is the value of $x$?

1. 6 cm
2. 4 cm
3. 10 cm
4. 5 cm

Q. Circles having the same centre but different radii are .

1. touching
2. intersecting
3. concentric
4. equal

Q. The perpendicular drawn from the centre of the circle to a chord divides the chord in the ratio .

1. 2:1
2. 1:2
3. 1:1

Q. In the given figures, O is the centre of the given circles. Match the values of $x$.

1. ${40}^{\circ }$
2. ${60}^{\circ }$
3. ${200}^{\circ }$