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Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d is
- a)1/2
- b)1
- c)2
- d)3
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Radii of the smallest and the largest circle passing through a point l...
⇒ |r2 - r2| is minimum when x is minimum.
|r2 - r2| = 1
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Radii of the smallest and the largest circle passing through a point l...
Let's assume that the rectangle has vertices A, B, C, and D, with AB as the longer side and BC as the shorter side.
To find the smallest circle passing through a point lying on the sides of the rectangle, we need to consider the two circles that pass through the given point and are tangent to two adjacent sides of the rectangle. Let's call the given point P.
1. Smallest Circle:
The smallest circle passing through point P and tangent to sides AB and AD will have its center on the perpendicular bisector of line segment AP. This is because the perpendicular bisector of a chord of a circle passes through the center of the circle.
So, let's construct the perpendicular bisector of line segment AP. This line will intersect side AB at a point, which we'll call M. The radius of the smallest circle passing through point P and tangent to sides AB and AD will be PM.
2. Largest Circle:
The largest circle passing through point P and tangent to sides AB and BC will have its center at the intersection of the diagonals of the rectangle. Let's call this point O. The radius of the largest circle passing through point P and tangent to sides AB and BC will be OP.
In conclusion, the radii of the smallest and largest circles passing through a point lying on the sides of a rectangle with vertices A, B, C, and D are PM and OP, respectively.
To find the smallest circle passing through a point lying on the sides of the rectangle, we need to consider the two circles that pass through the given point and are tangent to two adjacent sides of the rectangle. Let's call the given point P.
1. Smallest Circle:
The smallest circle passing through point P and tangent to sides AB and AD will have its center on the perpendicular bisector of line segment AP. This is because the perpendicular bisector of a chord of a circle passes through the center of the circle.
So, let's construct the perpendicular bisector of line segment AP. This line will intersect side AB at a point, which we'll call M. The radius of the smallest circle passing through point P and tangent to sides AB and AD will be PM.
2. Largest Circle:
The largest circle passing through point P and tangent to sides AB and BC will have its center at the intersection of the diagonals of the rectangle. Let's call this point O. The radius of the largest circle passing through point P and tangent to sides AB and BC will be OP.
In conclusion, the radii of the smallest and largest circles passing through a point lying on the sides of a rectangle with vertices A, B, C, and D are PM and OP, respectively.
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Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?
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Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?.
Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?.
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Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Radii of the smallest and the largest circle passing through a point lying on the sides of a rectangle with vertices (± 2, ± 1) and touching the circle x2 + y2 = 9, are r1 and r2 respectively. Let d = |r1 – r2| then minimum value of d isa)1/2b)1c)2d)3Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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