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Two parallel chords of a circle of radius 2 are at a distance 3 + 1 apart. If the chords subtend at the center, angles of π/k andk 2π/k , where k > 0, then the value of [k] is
{Note : [k] denotes the largest integer less than or equal to k}
[JEE 2010]
  • a)
    3
  • b)
    4
  • c)
    2
  • d)
    5
Correct answer is option 'A'. Can you explain this answer?
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Two parallel chords of a circle of radius 2 are at a distance 3 + 1 ap...










∴ 

⇒ k = 3
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Two parallel chords of a circle of radius 2 are at a distance 3 + 1 ap...
Let's call the two parallel chords AB and CD, with AB closer to the center of the circle.

Let O be the center of the circle. Let M be the midpoint of AB, and let N be the midpoint of CD. Let X be the intersection of AB and CD.

Since AB and CD are parallel, angle AMB is equal to angle CND. Also, angle AOB is equal to angle COD since they both subtend the same arc.

Let's call the distance from O to AB x. Since AB and CD are at a distance of 3 - 1 = 2 units apart, the distance from O to CD is also x.

Since OM is a radius of the circle, OM = 2. Similarly, ON = 2.

Since AM is a perpendicular bisector of AB, triangle OAM is a right triangle. Using the Pythagorean theorem, we have:

x^2 = 2^2 - 1^2 = 4 - 1 = 3
x = sqrt(3)

Therefore, the distance from O to each of AB and CD is sqrt(3) units.

Now, let's consider triangle OXM. Using the Pythagorean theorem, we have:

OM^2 = OX^2 + XM^2
2^2 = OX^2 + (1/2)^2
4 = OX^2 + 1/4
OX^2 = 16/4 - 1/4 = 15/4
OX = sqrt(15)/2

Therefore, angle MOX is equal to arctan(1/2) = 26.57 degrees.

Since angle AMB is equal to angle CND, and angle AOB is equal to angle COD, the angles subtended by AB and CD at the center are each equal to 2 * 26.57 degrees = 53.14 degrees.
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Two parallel chords of a circle of radius 2 are at a distance 3 + 1 apart. If the chords subtend at the center, angles of π/kandk 2π/k , where k > 0, then the value of [k] is{Note : [k] denotes the largest integer less than or equal to k}[JEE 2010]a)3b)4c)2d)5Correct answer is option 'A'. Can you explain this answer?
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Two parallel chords of a circle of radius 2 are at a distance 3 + 1 apart. If the chords subtend at the center, angles of π/kandk 2π/k , where k > 0, then the value of [k] is{Note : [k] denotes the largest integer less than or equal to k}[JEE 2010]a)3b)4c)2d)5Correct answer is option 'A'. 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 Two parallel chords of a circle of radius 2 are at a distance 3 + 1 apart. If the chords subtend at the center, angles of π/kandk 2π/k , where k > 0, then the value of [k] is{Note : [k] denotes the largest integer less than or equal to k}[JEE 2010]a)3b)4c)2d)5Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two parallel chords of a circle of radius 2 are at a distance 3 + 1 apart. If the chords subtend at the center, angles of π/kandk 2π/k , where k > 0, then the value of [k] is{Note : [k] denotes the largest integer less than or equal to k}[JEE 2010]a)3b)4c)2d)5Correct answer is option 'A'. Can you explain this answer?.
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