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Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 is
Correct answer is '10'. Can you explain this answer?
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Let C1 and C2 be concentric circles such that the diameter of C1 is 2 ...
Given, d + 2 = D ⇒ r + 1 = R
In the figure OT = r and OB = r + 1
OT ⊥ AB as AB is the tangent
OT bisects AB i.e., TB = 6/2 = 3
Now, in DOTB, OT2 + TB2 = OB2
∴ r2 + 32 = (r + 1)2⇒ r = 4
∴ D = 2(R ) = 2(r + 1) = 10cm
In the figure OT = r and OB = r + 1
OT ⊥ AB as AB is the tangent
OT bisects AB i.e., TB = 6/2 = 3
Now, in DOTB, OT2 + TB2 = OB2
∴ r2 + 32 = (r + 1)2⇒ r = 4
∴ D = 2(R ) = 2(r + 1) = 10cm
Most Upvoted Answer
Let C1 and C2 be concentric circles such that the diameter of C1 is 2 ...
Given:
- C1 and C2 are concentric circles.
- The diameter of C1 is 2 cm longer than that of C2.
- A chord of C1 has a length of 6 cm and is a tangent to C2.
To find:
The diameter of C1.
Solution:
Let's analyze the given information step by step to find the diameter of C1.
1. Definition of Concentric Circles:
Concentric circles are circles that have the same center. In this case, C1 and C2 are concentric circles.
2. Diameter of C1 and C2:
Let's assume the diameter of C2 is 'd'. Therefore, the diameter of C1 is 'd + 2' as given in the question.
3. Chord of C1:
A chord is a line segment that joins two points on a curve. In this case, the chord of C1 has a length of 6 cm.
4. Chord of C1 is a Tangent to C2:
A tangent is a line that touches a curve at only one point without crossing it. In this case, the chord of C1 is also a tangent to C2.
5. Relationship Between Chord and Tangent:
When a chord and a tangent intersect on a circle, the tangent line is perpendicular to the radius drawn to the point of intersection. In this case, the chord of C1 is perpendicular to the radius of C2 drawn to the point of intersection.
6. Properties of Tangent and Radius:
When a tangent and a radius intersect, the point of intersection is the point of contact. Therefore, the chord of C1 is also the diameter of C2.
7. Finding the Diameter of C2:
As the chord of C1 is the diameter of C2, its length is equal to the diameter of C2. Therefore, the diameter of C2 is 6 cm.
8. Finding the Diameter of C1:
The diameter of C1 is 2 cm longer than the diameter of C2. Therefore, the diameter of C1 is 6 cm + 2 cm = 8 cm.
Answer:
The diameter of C1 is 8 cm.
- C1 and C2 are concentric circles.
- The diameter of C1 is 2 cm longer than that of C2.
- A chord of C1 has a length of 6 cm and is a tangent to C2.
To find:
The diameter of C1.
Solution:
Let's analyze the given information step by step to find the diameter of C1.
1. Definition of Concentric Circles:
Concentric circles are circles that have the same center. In this case, C1 and C2 are concentric circles.
2. Diameter of C1 and C2:
Let's assume the diameter of C2 is 'd'. Therefore, the diameter of C1 is 'd + 2' as given in the question.
3. Chord of C1:
A chord is a line segment that joins two points on a curve. In this case, the chord of C1 has a length of 6 cm.
4. Chord of C1 is a Tangent to C2:
A tangent is a line that touches a curve at only one point without crossing it. In this case, the chord of C1 is also a tangent to C2.
5. Relationship Between Chord and Tangent:
When a chord and a tangent intersect on a circle, the tangent line is perpendicular to the radius drawn to the point of intersection. In this case, the chord of C1 is perpendicular to the radius of C2 drawn to the point of intersection.
6. Properties of Tangent and Radius:
When a tangent and a radius intersect, the point of intersection is the point of contact. Therefore, the chord of C1 is also the diameter of C2.
7. Finding the Diameter of C2:
As the chord of C1 is the diameter of C2, its length is equal to the diameter of C2. Therefore, the diameter of C2 is 6 cm.
8. Finding the Diameter of C1:
The diameter of C1 is 2 cm longer than the diameter of C2. Therefore, the diameter of C1 is 6 cm + 2 cm = 8 cm.
Answer:
The diameter of C1 is 8 cm.
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Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer?
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Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer?.
Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer?.
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Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer?, a detailed solution for Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer? has been provided alongside types of Let C1 and C2 be concentric circles such that the diameter of C1 is 2 cm longer than that of C2. If a chord of C1 has length 6 cm and is a tangent to C2, then the diameter, in cm, of C1 isCorrect answer is '10'. Can you explain this answer? theory, EduRev gives you an
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