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Circles CBSE Class 9

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Video Based Test funda (Please watch the above videos before attempting this assessment)
Question 1/20

Q 1. The number of radii which a circle can have is 

Solution

A circle can have infinite radii. 

Q 2. In a circle with radius 10 cm and centre O; if XY is a chord having length 10 cm, then XOY = 

Solution

Angles of an equilateral triangle measure 60o each.

Q 3. The region between an arc and a chord of a circle is called a 

Solution

The region between an arc and a chord of a circle is called a segment. 

Q 4. A part of a circle’s circumference is called a/an 

Solution

A part of a circle’s circumference is called an arc. 

Q 5. In a circle, chord AB = 10 cm and PQ = 8 cm. If O is the centre, then 

Solution

In a circle, chord AB > chord PQ. If O is the centre, then AOB >∠POQ.

Angles subtended by larger chords are larger than those subtended by smaller chords.

Q 6. Find the value of x in the given figure.   

Solution

Angles subtended in the same segment by the same arc are equal.

Q 7. Find the value of BAC if BD = DC and DBC = 50°.   

Solution

In BCD,

BD = DC

DCB = DBC

DCB = 50° 

DCB + DBC + BDC = 180° 

50° + 50° + BDC = 180° 

BDC = 80° 

BDC + BAC = 180° 

BAC = 100˚

Q 8. If XYZ is inscribed in a circle with centre O, XYZ = 30° and XZC = 90°, then YOZ = 

Solution

In XYZ,

XYZ = 30° and XZC = 90° 

So, YXZ = 60° 

Thus, YOZ = 2 × 60° = 120° 

The measure of an angle subtended by a chord at the centre of the circle is twice the measure of the angle subtended by it on the circumference. 

Q 9. The length of a chord which is at a distance of 8 cm from the centre of a circle of radius 17 cm is 

Solution

  

In OMA,

OM AB (a line drawn from the centre of a circle to the chord is perpendicular to the chord)

mM = 90° 

Here, OM = 8 cm and OB = 17 cm

By Pythagoras' theorem,

172 = 82 + MB2

289 - 64 = MB2

MB2 = 225

MB = 15 cm

AB = 2MB = 2 × 15 = 30 cm (A perpendicular drawn from the centre of a circle to a chord bisects the chord)

Q 10. AB and PQ are chords of a circle with centre O, such that AB = 10 cm and PQ = 8 cm; if OX and OY are the corresponding distances of the chords AB and PQ from the centre O, then 

Solution

The distance of a large chord from the centre of the circle is less than the distance of a smaller chord from the centre.

Q 11. Equal chords subtend ______ angles at the centre. 

Solution

Equal chords subtend equal angles at the centre.

Q 12. The perpendicular from the centre of a circle to a chord 

Solution

The perpendicular from the centre of a circle to a chord bisects the chord. 

Q 13. In a circle with centre O, AB is a chord of 3 cm and QR is a chord of 7 cm. So

Solution

As QR > AB, QOR > AOB.

Angles subtended by larger chords are larger than those subtended by smaller chords.

Q 14. Find the value of x in the given figure.   

Solution

Angle subtended by an arc on the centre is twice the measure of the angle subtended by the same arc on the circumference.

Q 15. An arc subtends an angle measuring 60o at the centre, so it will subtend an angle of ____ on the circumference. 

Solution

An arc subtends an angle measuring 60° at the centre, so it will subtend an angle of 30° on the circumference.

Q 16. Equal chords of _______ circles have the same distances from their respective centres. 

Solution

Equal chords of congruent circles have the same distances from their respective centres.

Q 17. In a circle with centre O and chord PQ, a perpendicular OX is drawn from the centre to chord PQ. So 

Solution

The shortest distance from a point to a line is the one passing through the point and perpendicular to the line.

Q 18. X is any point on the circle with centre O and chord AB. If AXB = 60°, then AOB =?

Solution

The measure of an angle subtended by a chord at the centre of the circle is twice the measure of the angle subtended by it on the circumference.

Q 19. A/an ___ of a circle is a line segment joining any two points on the circle. 

Solution

The chord of a circle is a line segment joining any two points on the circle. 

Q 20. If ABC is a right angle inscribed in a circle with centre O, then mAOC = 

Solution

The measure of an angle subtended by a chord at the centre of the circle is twice the measure of the angle subtended by it on the circumference.

Here, ABC is a right-angled triangle.

B = 90° 

AOC = 180° 

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