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The length of two parallel chords of a circle of radius 5cm are 6 cm and 8 cm in the same side of the centre. The distance between them is-
- a)2 cm
- b)1 cm
- c)1.5 cm
- d)3 cm
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The length of two parallel chords of a circle of radius 5cm are 6 cm ...
Here, O is the centre of the circle of radius 5 cm and AB and CD are two chord of length 8 cm and 6 cm respectively.
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∵ Perpendicular drawn from the centre of a circle to the chord bisects the chord.
∴ EB = 4 cm and FD = 3 cm
Now, In ΔΔ OEB
OB2 = OE2 + EB2
Most Upvoted Answer
The length of two parallel chords of a circle of radius 5cm are 6 cm ...
Given information:
- The radius of the circle is 5 cm.
- There are two parallel chords in the same side of the center.
- The length of one chord is 6 cm.
- The length of the other chord is 8 cm.
To find:
- The distance between the two chords.
Solution:
The distance between two parallel chords in a circle can be found using the formula:
Distance = √(4r² - (d₁ - d₂)²)
Where:
- r is the radius of the circle, which is 5 cm.
- d₁ is the length of one chord, which is 6 cm.
- d₂ is the length of the other chord, which is 8 cm.
Substituting the values into the formula:
Distance = √(4(5)² - (6 - 8)²)
= √(4(25) - (-2)²)
= √(100 - 4)
= √96
≈ 9.8 cm
Therefore, the distance between the two chords is approximately 9.8 cm.
But none of the given options match this result. Let's recheck the calculations.
The correct formula to find the distance between two parallel chords is:
Distance = √(4r² - (d₁ + d₂)²)
Using this formula, we get:
Distance = √(4(5)² - (6 + 8)²)
= √(4(25) - 14²)
= √(100 - 196)
= √(-96)
= √((-1)(96))
= √(-1) * √(96)
= i√96
Since the distance cannot be expressed as a real number, the only logical conclusion is that the distance between the two chords is imaginary or non-existent. Therefore, none of the given options are correct.
Note: It's important to double-check the calculations and use the correct formula when solving mathematical problems.
- The radius of the circle is 5 cm.
- There are two parallel chords in the same side of the center.
- The length of one chord is 6 cm.
- The length of the other chord is 8 cm.
To find:
- The distance between the two chords.
Solution:
The distance between two parallel chords in a circle can be found using the formula:
Distance = √(4r² - (d₁ - d₂)²)
Where:
- r is the radius of the circle, which is 5 cm.
- d₁ is the length of one chord, which is 6 cm.
- d₂ is the length of the other chord, which is 8 cm.
Substituting the values into the formula:
Distance = √(4(5)² - (6 - 8)²)
= √(4(25) - (-2)²)
= √(100 - 4)
= √96
≈ 9.8 cm
Therefore, the distance between the two chords is approximately 9.8 cm.
But none of the given options match this result. Let's recheck the calculations.
The correct formula to find the distance between two parallel chords is:
Distance = √(4r² - (d₁ + d₂)²)
Using this formula, we get:
Distance = √(4(5)² - (6 + 8)²)
= √(4(25) - 14²)
= √(100 - 196)
= √(-96)
= √((-1)(96))
= √(-1) * √(96)
= i√96
Since the distance cannot be expressed as a real number, the only logical conclusion is that the distance between the two chords is imaginary or non-existent. Therefore, none of the given options are correct.
Note: It's important to double-check the calculations and use the correct formula when solving mathematical problems.
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The length of two parallel chords of a circle of radius 5cm are 6 cm and 8 cm in the same side of the centre. The distance between them is-a)2 cmb)1 cmc)1.5 cmd)3 cmCorrect answer is option 'B'. Can you explain this answer?
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