What is the distance between two parallel tangents of a circle having radius 5 cm justify your answer?

Guys, does anyone know the answer?

get what is the distance between two parallel tangents of a circle having radius 4.5 cm? justify your answer. from screen.

What is the distance between two parallel tangents of a circle having radius 4.5 cm ?. Justify your answer.

Let the centre of the circle be O. Let the tangents AB and CD touch the circle at points M and N respectively. Draw seg OM and seg ON. Through O, draw line XY || line AB Line AB || line CD " ""……."(" Given ") Line XY || line AB " ""........"(" Construction ") :. line AB || line XY || line CD" "".......(i)" /OMA=/ONC=90^(@)" ""........"(" Tangent theorem ") Line AB|| line XY and line MO is the transversal, /AMO+/MOX=180^(@)" ""........"(" Interior angles theotem ") :.90^(@)+/MOX=180^(@) :./MOX=180^(@)-90^(@) :. /MOX=90^(@) Similarly /NOX=90^(@) :./MOX+/NOX=90^(@)+90^(@)=180^(@) :./MOX " and " /NOX are adjacent as well as supplementary. :./MOX " and " /NOX form linear pair. :. ray OM and ray ON are opposite rays. :. points M, O and N are collinear. :. MN is the distance between the parallel tangents AB and CD MN= 2xx " radius "" " "......."(" Diameter is twice the radius ") :.MN=2xx 4.5 :.MN=9 cm.

Home English Class 10 Maths Chapter Circle

What is the distance between t...

What is the distance between two parallel tangents of a circle having radius 4.5 cm ?. Justify your answer.

Answer

Step by step solution by experts to help you in doubt clearance & scoring excellent marks in exams.

Updated On: 12-03-2022

Get Answer to any question, just click a photo and upload the photo

and get the answer completely free,

UPLOAD PHOTO AND GET THE ANSWER NOW!

Watch 1000+ concepts & tricky questions explained!

Text Solution Answer

Distance between parallel tangents is 9 cm.

Solution

Let the centre of the circle be O. Let the tangents AB and CD touch the circle at points M and N respectively.

Draw seg OM and seg ON.

Through O, draw line XY || line AB

Line AB || line CD …….( Given ) …….( Given ) Line XY || line AB

........( Construction )

........( Construction )

∴ ∴

line AB || line XY || line CD

.......(i) .......(i) ∠OMA=∠ONC= 90 ∘

........( Tangent theorem )

∠OMA=∠ONC=90∘ ........( Tangent theorem )

Line AB|| line XY and line MO is the transversal,

∠AMO+∠MOX= 180 ∘

........( Interior angles theotem )

∠AMO+∠MOX=180∘ ........( Interior angles theotem )

∴ 90 ∘ +∠MOX= 180 ∘ ∴90∘+∠MOX=180∘ ∴∠MOX= 180 ∘ − 90 ∘ ∴∠MOX=180∘-90∘ ∴∠MOX= 90 ∘ ∴∠MOX=90∘ Similarly ∠NOX= 90 ∘ ∠NOX=90∘ ∴∠MOX+∠NOX= 90 ∘ + 90 ∘ = 180 ∘

∴∠MOX+∠NOX=90∘+90∘=180∘

∴∠MOX and ∠NOX ∴∠MOX and ∠NOX

are adjacent as well as supplementary.

∴∠MOX and ∠NOX ∴∠MOX and ∠NOX form linear pair. ∴ ∴

ray OM and ray ON are opposite rays.

∴ ∴

points M, O and N are collinear.

∴MN ∴MN

is the distance between the parallel tangents AB and CD

MN=2× radius .......( Diameter is twice the radius )

MN=2× radius .......( Diameter is twice the radius )

∴MN=2×4.5 ∴MN=2×4.5 ∴MN=9 ∴MN=9 cm.

Related Videos

43959169 7.7 K+ 8.4 K+ 2:10

43959174 7.3 K+ 9.6 K+ 2:17

43959175 3.1 K+ 5.0 K+ 2:10

42340697 4.5 K+ 9.0 K+ 2:11

42341959 9.3 K+ 9.3 K+ 2:17

42341958 3.7 K+ 8.5 K+ 2:45

Show More

Very Important Questions

Distinction between pairs of compounds

3-Bromoprop-1-ene (C H 2 =CH−C H 2 Br) (CH2=CH-CH2Br) and 1-Bromopropane (C H 3 C H 2 C H 2 Br) (CH3CH2CH2Br) . (a) B r 2 Br2 test.

(b) Baeyer's reagent test.

Time required to decompose

S O 2 C l 2 SO2Cl2

to half of its initial amount is 60 minutes. If the decomposition is a first order reaction, calculate the rate constant of the reaction.

Is there any reaction for which reaction rate does not decrease with time?

In the reaction A → →

B , if the concentration of A is plotted against time, the curves obtained will be as shown in Fig. 1 and 2. Predict the order of the reactions.

The rate constant of a reaction increases linearly with increase in temperature.

The rate constant of a first order reaction is

4.5× 10 −2 sec −1 4.5×10-2sec-1

What will be the time required for the initial concentration of 0.4 M of the reactant to be reduced to 0.2 M ?

FAQs on Circle

What is Circle ?

Position of a point at circumference with respect to centre of a circle

Circular Disc and Concentric circles

Radius; Perimeter and Area

Arc of a Circle Length of an Arc Central Angle Major and Minor Arc Chord of a circle Diameter

अधिक देखने के लिए क्लिक करें

स्रोत : www.doubtnut.com

What is the distance between two parallel tangents of a circle having radius 4.5 cm?

What is the distance between two parallel tangents of a circle having radius 4.5 cm? Justify your answer.

What is the distance between two parallel tangents of a circle having radius 4.5 cm?

← Prev Question Next Question →

1 Answer

← Prev Question Next Question →

Find MCQs & Mock Test

Free JEE Main Mock Test

Free NEET Mock Test

Class 12 Chapterwise MCQ Test

Class 11 Chapterwise Practice Test

Class 10 Chapterwise MCQ Test

Class 9 Chapterwise MCQ Test

Class 8 Chapterwise MCQ Test

Class 7 Chapterwise MCQ Test

Related questions

अधिक देखने के लिए क्लिक करें

स्रोत : www.sarthaks.com

What is the Distance Between Two Parallel Tangents of a Circle Having Radius 4.5 Cm ? Justify Your Answer.

What is the Distance Between Two Parallel Tangents of a Circle Having Radius 4.5 Cm ? Justify Your Answer.

Advertisement Remove all ads Sum

What is the distance between two parallel tangents of a circle having radius 4.5 cm ? Justify your answer.

Advertisement Remove all ads

SOLUTION 1

In the given figure, O is the centre of the circle. Line PT and line QR are two parallel tangents to the circle at P and Q, respectively.

∴ ∠OPT + ∠OQR = 180º    ......(Sum of adjacent interior angles on the same side of the transversal is supplementary)

⇒ POQ is a straight line segment.

∴ PQ is the diameter of the circle.

PQ = Distance between the parallel tangents PT and QR

= 2 × Radius = 2 × 4.5 = 9 cm

Thus, the distance between two parallel tangents of the circle is 9 cm.

SOLUTION 2

Let the lines PQ and RS be the two parallel tangents to circle at M and N respectively.

Through centre O, draw line AB || line RS.

OM = ON = 4.5     ......[Given]

Line AB || line RS   ......[Construction]

Line PQ || line RS  ......[Given]

∴ Line AB || line PQ || line RS

Now, ∠OMP = ∠ONR = 90°    ......(i) [Tangent theorem]

For line PQ || line AB,

∠OMP = ∠AON = 90°   ......(ii) [Corresponding angles and from (i)]

For line RS || line AB,

∠ONR = ∠AOM = 90° (iii)   ......Corresponding angles and from (i)]

∠AON + ∠AOM = 90° + 90°    ......[From (ii) and (iii)]

∴ ∠AON + ∠AOM = 180°

∴ ∠AON and ∠AOM form a linear pair.

∴ Ray OM and ray ON are opposite rays.

∴ Points M, O, N are collinear.    ......(iv)

∴ MN = OM + ON       ......[M−O–N, From (iv)]

∴ MN = 4.5 + 4.5 ∴ MN = 9 cm

∴ Distance between two parallel tangents PQ and RS is 9 cm.

Concept: Tangent to a Circle

Is there an error in this question or solution?

Chapter 3: Circle - Q.4

Q 3 Q 2 Q 4

APPEARS IN

SCERT Maharashtra Question Bank 10th Standard SSC Mathematics 2 Geometry Maharashtra State Board 2021

Chapter 3 Circle Q.4 | Q 3

Balbharati Mathematics 2 Geometry 10th Standard SSC Maharashtra State Board

Advertisement Remove all ads

अधिक देखने के लिए क्लिक करें

स्रोत : www.shaalaa.com