Defence Exam > Defence Questions > The distance between the centers of two circl...
Start Learning for Free
The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?
- a)12 cm
- b)11 cm
- c)10 cm
- d)9.5 cm
Correct answer is option 'A'. Can you explain this answer?
| FREE This question is part of | Download PDF Attempt this Test |
Verified Answer
The distance between the centers of two circles having radii 9 cm and ...
Since the distance between the centers is 13 cm, they touch each other.
CD is the common tangent
CA = AB and AD = AB [∵ Tangents drawn from a common point are same]
∴ CD = CA + AD = 2AB
⇒ ∠PAC = ∠BAP
∴ CD = CA + AD = 2AB
⇒ ∠PAC = ∠BAP
⇒ ∠DAQ = ∠BAQ [∵ Line drawn from the center divides the angle between the tangents]
⇒ ∠CAP + ∠PAB + ∠BAQ + ∠DAQ = 180° [Angle is straight line is 180°]
⇒ 2 × (∠PAB + ∠BAQ) = 180°
∴ ∠PAB + ∠BAQ = 90°
⇒ tan∠PAB = PB/AB
⇒ tan∠BAQ = tan(90 - ∠PAB) = cot∠PAB = QB/AB
⇒ tan∠PAB × cot∠PAB = 1
⇒ PB/AB × QB/AB = 1
⇒ 9/AB × 4/AB = 1
⇒ AB2 = 36
∴ AB = 6 cm
∴ CD = 2AB = 12 cm
⇒ 2 × (∠PAB + ∠BAQ) = 180°
∴ ∠PAB + ∠BAQ = 90°
⇒ tan∠PAB = PB/AB
⇒ tan∠BAQ = tan(90 - ∠PAB) = cot∠PAB = QB/AB
⇒ tan∠PAB × cot∠PAB = 1
⇒ PB/AB × QB/AB = 1
⇒ 9/AB × 4/AB = 1
⇒ AB2 = 36
∴ AB = 6 cm
∴ CD = 2AB = 12 cm
Most Upvoted Answer
The distance between the centers of two circles having radii 9 cm and ...
To find the length of the direct common tangent of two circles, we can use the Pythagorean theorem and the fact that the radii form a right triangle with the length of the direct common tangent as the hypotenuse.
Let's label the centers of the circles as O1 and O2, and the radii as r1 = 9 cm and r2 = 4 cm. The distance between the centers of the circles is given as 13 cm.
- Label the centers of the circles and the radii
- Use the Pythagorean theorem to find the length of the direct common tangent
Using the Pythagorean theorem, we have:
(Length of direct common tangent)^2 = (Distance between centers)^2 - (Sum of radii)^2
Let's substitute the given values into the equation:
(Length of direct common tangent)^2 = (13 cm)^2 - (9 cm + 4 cm)^2
(Length of direct common tangent)^2 = 169 cm^2 - 169 cm^2
(Length of direct common tangent)^2 = 0 cm^2
Since the square of the length of the direct common tangent is 0, it means that the length itself is also 0. This implies that the two circles are touching each other at a single point, and there is no direct common tangent between them.
Therefore, the correct answer is None of the above (0 cm).
Let's label the centers of the circles as O1 and O2, and the radii as r1 = 9 cm and r2 = 4 cm. The distance between the centers of the circles is given as 13 cm.
- Label the centers of the circles and the radii
- Use the Pythagorean theorem to find the length of the direct common tangent
Using the Pythagorean theorem, we have:
(Length of direct common tangent)^2 = (Distance between centers)^2 - (Sum of radii)^2
Let's substitute the given values into the equation:
(Length of direct common tangent)^2 = (13 cm)^2 - (9 cm + 4 cm)^2
(Length of direct common tangent)^2 = 169 cm^2 - 169 cm^2
(Length of direct common tangent)^2 = 0 cm^2
Since the square of the length of the direct common tangent is 0, it means that the length itself is also 0. This implies that the two circles are touching each other at a single point, and there is no direct common tangent between them.
Therefore, the correct answer is None of the above (0 cm).
|
Explore Courses for Defence exam
|
|
Similar Defence Doubts
The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer?
Question Description
The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer?.
The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer?.
Solutions for The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Defence.
Download more important topics, notes, lectures and mock test series for Defence Exam by signing up for free.
Here you can find the meaning of The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice The distance between the centers of two circles having radii 9 cm and 4 cm is 13 cm. What is the length of the direct common tangent of these circles?a)12 cmb)11 cmc)10 cmd)9.5 cmCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice Defence tests.
|
|
Explore Courses for Defence exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup