Students can Download Class 10 Maths Chapter 4 Circles Additional Questions Questions, Notes Pdf, KSEEB Solutions for Class 10 Maths helps you to revise the complete Karnataka State Board Syllabus and score more marks in your in examinations

## Karnataka State Syllabus Class 10 Maths Chapter 4 Circles Additional Questions

I. Multiple Choice Questions:

Question 1.

Line segment joining the centre and a point on the circle is called

(a) radius

(b) diameter

(c) Chord

(d) Arc

Answer:

(a) radius

Question 2.

Part of a circle is called

(a) Chord

(b) diameter

(c) Segment

(d) Arc

Answer:

(d) Arc

Question 3.

The biggest chord in a circle is called

(a) radius

(b) diameter

(c) chord

(d) Arc

Answer:

(b) diameter

Question 4.

The region, bounded by a major arc and a chord is called

(a) Segment

(b) major segment

(c) minor segment

(d) major arc

Answer:

(b) major segment

Question 5.

The length of the biggest chord is 8 cm then the value of radius is

(a) 8 cm

(b) 4 cm

(c) 3 cm

(d) 5 cm

Answer:

(b) 4 cm

Question 6.

How many radius can be drawn in circle

(a) 1

(b) 2

(c) only 3

(d) many

Answer:

(d) many

Question 7.

An angle in a semicircle is.

(a) 60°

(b) 30°

(c) 90°

(d) 180°

Answer:

(c) 90°

Question 8.

Equal chords of a circle are.

(a) Equidistant from the centre.

(b) Equal

(c) Unequal

(d) Not equidistant from the centre

Answer:

(b) Equal

Question 9.

If the length of the chord increases its perpendicular distance from the centre.

(a) Increases

(b) Decreases

(c) Equal

(d) Constant

Answer:

(b) Decreases

Question 10.

The perpendicular distance between the biggest chord and the centre is.

(a) zero

(b) Equal

(c) 9 cm

(d) 10cm

Answer:

(a) zero

Question 11.

In a circle angles in the major segment are called.

(a) Obtuse angles

(b) Acute angles.

(c) Right angles

(d) Complete angle

Answer:

(b) Acute angles.

Question 12.

In a circle angles in the minor segment are called.

(a) Obtuse angles

(b) Acute angles.

(c) Right angles

(d) zero angle

Answer:

(a) Obtuse angles

Question 13.

In a circle angles in the same segment are

(a) Not equal

(b) Right angles

(c) Equal

(d) zero angle.

Answer:

(c) Equal

Question 14.

Circles having the same centre but different radii are called.

(a) Congruent circles

(b) Concentric circles

(c) Equal circles

(d) None of these

Answer:

(b) Concentric circles

Question 15.

Circles having same radii but different centres are called

(a) Congruent circles

(b) Concentric circles

(c) Equal circles.

(d) Intersecting circles

Answer:

(a) Congruent circles

Question 16.

The number of circles are drawn through three non-collinear points in a plane is.

(a) 1

(b) 2

(c) 3

(d) 4

Answer:

(a) 1

Question 17.

A line which intersects a circle in two points is called

(a) A secant

(b) A chord

(c) An arc

(d) A tangent

Answer:

(a) A secant

Question 18.

A line which intersects a circle in only one point is called

(a) A secant

(b) A tangent

(c) A chord

(d) A diameter

Answer:

(b) A tangent

Question 19.

A tangent to a circle intersects the circle is

(a) one point only

(b) Two points

(c) No point

(d) Three points

Answer:

(a) one point only

Question 20.

A secant of a circle intersects the circle in

(a) only one point

(b) Two points

(c) Three points

(d) No point

Answer:

(b) Two points

Question 21.

The point where a tangent line intersects a circle is called the

(a) centre

(b) point of contact

(c) End-point

(d) None of these

Answer:

(b) point of contact

Question 22.

The angle between the tangent at any point of a circle and the radius through the point of contact is

(a) 60°

(b) 90°

(c) 45°

(d) 30°

Answer:

(b) 90°

Question 23.

How many tangents can be drawn to a circle at any point of it?

(a) 1

(b) 2

(c) 3

(d) None of these

Answer:

(a) 1

Question 24.

How many parallel tangents can a circle have at the most?

(a) 1

(b) 2

(c) 4

(d) 3

Answer:

(b) 2

Question 25.

Two circles of radii 5 cm and 3 cm touch each other externally. The distance between their centres is

(a) 5 cm

(b) 3 cm

(c) 2 cm

(d) 8 cm

Answer:

(d) 8 cm

Question 26.

Two circles of radii 5 cm and 3 cm touch each other internally. The distance between their centres is

(a) 5 cm

(b) 3 cm

(c) 2 cm

(d) 8 cm

Answer:

(c) 2 cm

Question 27.

The tangents at the endpoints of a diameter of circle are

(a) perpendicular

(b) parallel

(c) intersecting

(d) inclined at 60°

Answer:

(b) parallel

Question 28.

The length of the tangent from a point A at distance 5 cm from the centre of the circle is 4 cm. The radius of the circle is

(a) 3 cm

(b) 2 cm

(c) 5 cm

(d) 4 cm

Answer:

(a) 3 cm

Question 29.

Two concentric circles of radii 5 cm, and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

(a) 8 cm

(b) 6 cm

(c) 4 cm

(d) 10 cm

Answer:

(a) 8 cm

Question 30.

How many tangent lines can be drawn to a circle from a point outside the circle?

(a) 1

(b) 2

(c) 3

(d) 4

Answer:

(b) 2

Question 31.

How many tangents can be drawn to a circle have

(a) 2

(b) infinitely many

(c) one

(d) no

Answer:

(b) infinitely many

Question 32.

In the following figure, |PBA is

(a) 60°

(b) 30°

(d) 45°

(d) none of these

Answer:

(a) 60°

Question 33.

In the following figure, Find AP if AB = 5 cm

(a) 5 cm

(b) 4 cm

(c) 3 ccm

(d) 2 cm

Answer:

(a) 5 cm

Question 34.

In the following figure, find the perimeter of A APQ if AB = 6 cm.

(a) 10 cm

(b)12cm

(c) 15 cm

(d) 6 cm

Answer:

(b)12cm

Question 35.

In the following Figure, find the length of the chord AB if PA = 4 cm and OP = 3 cm.

(a) 2 cm

(b) 4 cm

(c) 10cm

(d) 5 cm

Answer:

(c) 10cm

II. Short Answer Questions:

Question 1.

Define concentric circles.

Answer:

Circles which are having same centre and different radii are called concentric circles.

Question 2.

Define congruent circles.

Answer:

Circles which are having same radii & different centres are called congruent circles.

Question 3.

Define the sector of a circle.

Answer:

The region bounded by an arc of a circle and its two bounding radii is called sector.

Question 4.

Name the biggest chord of a circle.

Answer:

Diameter

Question 5.

Write the formula to find the perimeter of a circle.

Answer:

Circumference = C = 2nx.

Question 6.

Name the angle formed in a semi-circle is

Answer:

Right angle

Question 7.

Name the angle formed in a major segment.

Answer:

Acute angle

Question 8.

Name the angle formed in a minor segment.

Answer:

Obtuse angle.

Question 9.

The length of the tangent to a circle from a point P, which is 25 cm away from the centre, is 24 cm. What is the radius of the circle?

Answer:

Question 10.

In a quadrilateral, ABCD circumscribes a circle with centre O. If ∠AOB = 110°, then find ∠COD.

Answer:

Question 11.

Write the relationship between radius and diameter.

Answer:

d = 2r (or) r = d/2

Question 12.

Angles formed in a same segment are ________

Answer:

Equal

III. Long Answer Questions:

Question 1.

In the following figure if ∠DAB = 60°

and ∠ACB = 70°, find the measure of ∠DBA.

Answer:

Question 2.

Prove that the perpendicular from the centre of a circle to a chord, bisect the chord.

Answer:

AB is the chord of a circle with centre O and OD ⊥ AB. We have to prove that AD = DB

In ∆ ODA and ∆ ODB.

OA = OB (radii)

OD = OD (common)

∠ODA = ∠ODB = 90° (OD ⊥ AB)

∆ ODA = ∆ ODB (R H S)

AD = DB [C.P.C.T].

Question 3.

If two equal chords of a circle intersect within the circle, prove that the segments of an chord are equal to corresponding segment of the other chord.

Answer:

OL ⊥ AB and OM ⊥ CD are drawn and OP is joined.

In ∆ OLP and ∆ OMP, since equal chords are at equal distance from centres.

OL = OM (OP common)

∠OLP = ∠OMP =90°

∆ OPL ≅ ∆ OPM. (R H S)

=> PL = PM [C.P.C.T]

But, AL = CM

=> AL – PL = CM – PM

=> AP = CP

Also, AB – AP = CD – CP

∴BP = DP

Thus, corresponding segments are equals.

Question 4.

If two interesting chords of a circle make equal angel with that: diameter passing through their point of intersecting. Prove that the chords are equal.

Answer:

OM ⊥ AB and ON⊥CD

In ∆ OME and ∆ ONE

OE = OE (common)

∴ By A AS congruence

∆ OME ≅ ∆ ONE

OM = ON (C.P.C.T)

∴ AB = GD [Distance between the center to the chords equal.]

∴ Length of the chords are equal.

Question 5.

Two concentric circles of radii 13 cm and 5 cm are drawn. Find the length of the chord of the outer circle which touches the inner circle.

Answer:

In A OPB [P = 90°

OB2 = OP2 + BP2

(13)2 = (5)2 + BP2

BP2 = 165 – 25 = 144

AB = 2BP = 2 x 12 = 24cm

Question 6.

Tangents AP and AQ are drawn to circle with centre O, from an external point A. Prove that ∠PAQ = 2∠OPQ

Answer:

‘O’ is the center of a circle.

AP & AQ are tangents.

In A POQ, OP = OQ [radius]

Question 7.

Circles C_{1} and C_{2} touch internally at a point A and AB is a chord at the circle C_{1} intersecting C_{2} at P. Prove that AP = PB.

Answer:

Join OA, OP and OB.

HYP OA = HYP OB [radii]

OP = OP [common]

∆ OAP ≅ ∆ OPB [by RHS theorem]

AP = PB [C.P.C.T]

Question 8.

A circle is touching the side BC of ∆ ABC at P. AB and AC when produced are touching the circle at Q and R respectively. Prove that AQ = V_{2} (Perimeter of ∆ ABC)

Answer:

AQ = AR → (1) [tangents drawn from A]

BP = BQ → (2) [tangents drawn from B]

CQ = CR → (3) [tangents drawn from C]

Perimeter of ∆ ABC = AB + BC + AC

= AB + BP + PC + AC

= AB + BQ + CR + AC

[From (1), (2) & (3)]

= AQ + AR

= AQ + AQ [∴ using(1)]

Perimeter of ∆ ABC = 2 AQ

AQ = 1/2 (Perimeter of ∆ ABC)

Question 9.

A straight line drawn through the point of contact of two circles with centres A and B intersect the circles at P and Q respectively. Show that AP and BQ are parallel.

Answer:

In ∆ APC

AP = AC [radii of same circle]

Question 10.

Two circles with centres X and Y touch each other externally at P. Two diameters AB and CD are drawn one in each circle parallel to other. Prove that B, P and C are coliinear.

Answer:

∴ APD and BPC are two intersecting lines

∴ BPC is a straight line

∴ B, P, C are coliinear.