Theorem on Tangents MCQ Quiz in मल्याळम - Objective Question with Answer for Theorem on Tangents - സൗജന്യ PDF ഡൗൺലോഡ് ചെയ്യുക

Last updated on Mar 11, 2025

നേടുക Theorem on Tangents ഉത്തരങ്ങളും വിശദമായ പരിഹാരങ്ങളുമുള്ള മൾട്ടിപ്പിൾ ചോയ്സ് ചോദ്യങ്ങൾ (MCQ ക്വിസ്). ഇവ സൗജന്യമായി ഡൗൺലോഡ് ചെയ്യുക Theorem on Tangents MCQ ക്വിസ് പിഡിഎഫ്, ബാങ്കിംഗ്, എസ്എസ്‌സി, റെയിൽവേ, യുപിഎസ്‌സി, സ്റ്റേറ്റ് പിഎസ്‌സി തുടങ്ങിയ നിങ്ങളുടെ വരാനിരിക്കുന്ന പരീക്ഷകൾക്കായി തയ്യാറെടുക്കുക

Latest Theorem on Tangents MCQ Objective Questions

Top Theorem on Tangents MCQ Objective Questions

Theorem on Tangents Question 1:

In the given figure, chords XY and PQ intersect each other at point L. Find the length of XY (in cm).

F3 SSC Savita 12-1-24 D2

  1. 21
  2. 20
  3. 22
  4. 23

Answer (Detailed Solution Below)

Option 3 : 22

Theorem on Tangents Question 1 Detailed Solution

Calculation

By the theorem,

F3 SSC Savita 12-1-24 D2

LQ × LP = LY × LX

Let the length of XY be x.

⇒ 5 × 15 = 3 × (3 + x)

⇒ 25 = x + 3

⇒ x = 22

The length of XY is 22.

Theorem on Tangents Question 2:

Two circles touch each other externally. The radius of the first circle with centre O is 6 cm. The radius of the second circle with centre P is 3 cm. Find the length of their common tangent AB.

  1. 3√2 cm
  2. 4√2 cm
  3. 6√3 cm
  4. 6√2 cm

Answer (Detailed Solution Below)

Option 4 : 6√2 cm

Theorem on Tangents Question 2 Detailed Solution

Given:

The radius of smaller circle = 3 cm

The radius of large circle = 6 cm

Formula used:

Direct common tangent = 2 × √(R × r)

Where, R = radius of large circle;

and r = radius of the small circle

Calculation:

Direct common tangent = 2 × √(R × r)

⇒ 2 × √(3 × 6)

⇒ 2 × 3 × √2 = 6√2 cm

∴ The correct answer is 6√2 cm.

Theorem on Tangents Question 3:

In the given figure, if PA and PB are tangents to the circle with centre O such that ∠APB = 54°, then OBA = ________.

F1 SSC Amit A 09-03-2023 D10

  1. 27°
  2. 40°
  3. 30°
  4. 35°

Answer (Detailed Solution Below)

Option 1 : 27°

Theorem on Tangents Question 3 Detailed Solution

Given:

PA and PB are tangents to the circle with center O such that ∠APB = 54°

Calculation:

F1 SSC Amit A 09-03-2023 D12

We know that the radius and tangent are perpendicular at their point of contact.

So,

∠PAO = ∠PBO = 90°

So,

∠AOB = 360 - 54 - 180

⇒ 126°

Also AO = OB = Radius

So, ∠OAB = ∠OBA = 54/2

⇒ 27°

∴ The required answer is 27°

Theorem on Tangents Question 4:

If PT is a tangent at T to a circle whose centre is O and OP = 17 cm and OT = 8 cm, find the length of the tangent segment PT

  1. 13 cm
  2. 14 cm
  3. 16 cm
  4. 15 cm

Answer (Detailed Solution Below)

Option 4 : 15 cm

Theorem on Tangents Question 4 Detailed Solution

Given:

PT is a tangent to a circle, whose centre is O.

OP = 17 cm

OT = 8 cm

Formula used:

Screenshot 2023-02-27 184313

Pythagoras Theorem: In a right-angle triangle, the hypotenuse is equal to - 

OP2 = OT2 + TP2

Calculation:

This, the length of the tangent TP is equal to:

TPOP2 - OT2  

TP(17)2 - (8)2  

TP= 289 - 64

TP= 225 

TP = 225 = 15

∴ The length of the tangent segment PT is equal to 15 cm.

Theorem on Tangents Question 5:

The diameters of two circles are 12 cm and 20 cm, respectively and the distance between their centres is 16 cm. Find the number of common tangents to the circles.

  1. 2
  2. 3
  3. 1
  4. 4

Answer (Detailed Solution Below)

Option 2 : 3

Theorem on Tangents Question 5 Detailed Solution

Given:

The diameters of the two circles are 12 cm and 20 cm

The distance between their centres is 16 cm

Calculation:

F1 SSC Amit A 09-03-2023 D5

F2 SSC Mrunal 02.05.2023 D1

According to the diagram,

The two circles are touching each other externally

So, the number of common tangents will be 3

∴ The required answer is 3.

Theorem on Tangents Question 6:

Let C be a circle with centre O and P be an external point to C. Let PA and PB be two tangents to C with A and B being the points of tangency, respectively. If PA and PB are inclined to each other at an angle of 60º, then find ∠POA.

  1. 40º
  2. 60º
  3. 80º
  4. 30º

Answer (Detailed Solution Below)

Option 2 : 60º

Theorem on Tangents Question 6 Detailed Solution

Given:

∠APB = 60º

Formula used:

In ΔOAP and ΔOBP:

OA = OB (radii of the circle)

AP = BP (length of tangents from an external point)

OP = OP (common side)

By SSS congruence, ΔOAP ≅ ΔOBP

∠POA = ∠POB

∠OPA = ∠OPB

Therefore, OP is the angle bisector of ∠APB and ∠AOB

Hence, ∠OPA = ∠OPB = 1/2 (∠APB )

= 1/2 × 60°

= 30°

Calculation:

qImage673492e3114a01f9d7f968d7

By angle sum property of a triangle,

In ΔOAP

∠A + ∠POA + ∠OPA = 180°

OA ⊥ AP     (The tangent at any point of a circle is perpendicular to the radius through the point of contact.)

Therefore, ∠A = 90°

90° + ∠POA + 30° = 180°

120° + ∠POA = 180°

∠POA = 180° - 120°

∠POA = 60°

Therefore, Option (2) i.e 60° is the correct answer.

Theorem on Tangents Question 7:

P and Q are centres of two circles whose radii are 7 cm and 3 cm, respectively. If the direct common tangents to the circles meet PQ extended at A, then A divides PQ ________.

  1. externally in the ratio 3 : 7
  2. internally in the ratio 3 : 7
  3. externally in the ratio 7 : 3
  4. internally in the ratio 7 : 3

Answer (Detailed Solution Below)

Option 3 : externally in the ratio 7 : 3

Theorem on Tangents Question 7 Detailed Solution

Given:

Radius of circle with center P = 7 cm.

Radius of circle with center Q = 3 cm.

Formula Used:

Ratio of division of line segment by external tangents = Ratio of radii of circles

Calculation:

Let the direct common tangents to the circles meet PQ extended at A.

Task Id 897 (5)

Since the tangents are direct common tangents, they will divide the line segment PQ externally in the ratio of the radii of the circles.

Ratio of radii of the circles = 7:3

Therefore, A divides PQ externally in the ratio 7:3

The correct answer is option 3.

Theorem on Tangents Question 8:

Find the value of x in the given figure where TF ( tangent on point T) = 15 cm, FB = 2x + 3 cm, FA = 9 cm.

F1 SSC Arbaz 6-10-23 D15

  1. 21 cm
  2. 18 cm
  3. 15 cm
  4. 11 cm

Answer (Detailed Solution Below)

Option 4 : 11 cm

Theorem on Tangents Question 8 Detailed Solution

Given:-  

TF = 15 cm, FB = 2x + 3 cm and FA = 9 cm

Concept used:-

According to the tangent theorem,

TF2 = FA × FB

Calculation:-

TF2 = FA × FB

 225 = 9 × (2x + 3) 

⇒ (2x + 3) = 25

⇒ x  = 11cm 

∴ The required result will be 11.   

Theorem on Tangents Question 9:

The number of parallel tangents of a circle with a given tangent is:

  1. 1
  2. 2
  3. 3
  4. 4

Answer (Detailed Solution Below)

Option 1 : 1

Theorem on Tangents Question 9 Detailed Solution

Concept used:

F1 Varun.G 25-08-2020 Savita D2

Explanation:

The largest chord in a circle is the diameter. This meets the circle at two points. The points of tangency lie on the two points where the diameter meets the circle.

∴ A circle can have 2 parallel tangents at most.

So, only one parallel tangent is possible for a given tangent.

Important points:

This diameter meets the circle in exactly two points. So there is no more space for a third or more parallel tangents

Theorem on Tangents Question 10:

What is the number of common tangents that can be drawn to two circles that touch each other externally?

  1. 2
  2. 4
  3. 3
  4. 1

Answer (Detailed Solution Below)

Option 3 : 3

Theorem on Tangents Question 10 Detailed Solution

Calculation : 

F1 Other Arbaz 30-10-23 D16

∴ The correct answer is 3.

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