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In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance between the chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is :
- a)23 cm
- b)30 cm
- c)15 cm
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
In a circle of radius 17 cm, two parallel chords are drawn on opposite...
Given a circle, with centre O having a radius = 17 cm and two parallel chords, AB and CD, 23 cm apart.
Length of one chord, AB = 16 cm.
Length of the second chord, CD is to be determined.
Distance of chord AB from O = [17^2-(16/2)^2]^0.5 = [289–64]^0.5 = 225^0.5 = 15 cm.
Distance of CD from O = 23 - 15 = 8 cm
Length of CD = 2*[17^2–8^2]^0.5 = 2*[289–64]^0.5 = 2*15 = 30 cm.
The second chord, CD, is 30 cm long.
Most Upvoted Answer
In a circle of radius 17 cm, two parallel chords are drawn on opposite...
Understanding the Problem
In a circle with a radius of 17 cm, two parallel chords are positioned on either side of a diameter. The distance between these chords is 23 cm, and the length of one chord is known to be 16 cm. We need to find the length of the other chord.
Diagram and Setup
- Let the center of the circle be O.
- Let the distance from the center O to the first chord (length 16 cm) be d1.
- The distance from O to the second chord (length to be determined) will be d2.
- The distance between the two chords is given as 23 cm, so:
d1 + d2 = 23 cm.
Calculating the Distance from Center to Chord
- For the first chord of length 16 cm, we can calculate d1 using the relationship of chords in a circle. The formula relating the radius (r), distance from the center (d), and half the chord length (c) is:
r² = d² + c².
Here, c = 8 cm (half of 16 cm).
- Substituting the values:
17² = d1² + 8²
289 = d1² + 64
d1² = 225
d1 = 15 cm.
Finding the Distance for the Other Chord
- Now, using the distance relationship:
d1 + d2 = 23 cm.
15 cm + d2 = 23 cm.
d2 = 8 cm.
Calculating the Length of the Second Chord
- Now, use d2 to find the length of the second chord.
Using the relationship again:
17² = d2² + c2², where c2 is half the length of the second chord.
- Substituting the known values:
289 = 8² + c2²
289 = 64 + c2²
c2² = 225
c2 = 15 cm.
Therefore, the length of the second chord = 2 * c2 = 30 cm.
Conclusion
The length of the other chord is 30 cm, confirming option 'B'.
In a circle with a radius of 17 cm, two parallel chords are positioned on either side of a diameter. The distance between these chords is 23 cm, and the length of one chord is known to be 16 cm. We need to find the length of the other chord.
Diagram and Setup
- Let the center of the circle be O.
- Let the distance from the center O to the first chord (length 16 cm) be d1.
- The distance from O to the second chord (length to be determined) will be d2.
- The distance between the two chords is given as 23 cm, so:
d1 + d2 = 23 cm.
Calculating the Distance from Center to Chord
- For the first chord of length 16 cm, we can calculate d1 using the relationship of chords in a circle. The formula relating the radius (r), distance from the center (d), and half the chord length (c) is:
r² = d² + c².
Here, c = 8 cm (half of 16 cm).
- Substituting the values:
17² = d1² + 8²
289 = d1² + 64
d1² = 225
d1 = 15 cm.
Finding the Distance for the Other Chord
- Now, using the distance relationship:
d1 + d2 = 23 cm.
15 cm + d2 = 23 cm.
d2 = 8 cm.
Calculating the Length of the Second Chord
- Now, use d2 to find the length of the second chord.
Using the relationship again:
17² = d2² + c2², where c2 is half the length of the second chord.
- Substituting the known values:
289 = 8² + c2²
289 = 64 + c2²
c2² = 225
c2 = 15 cm.
Therefore, the length of the second chord = 2 * c2 = 30 cm.
Conclusion
The length of the other chord is 30 cm, confirming option 'B'.
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In a circle of radius 17 cm, two parallel chords are drawn on opposite sides of a diameter. The distance betweenthe chords is 23 cm. If the length of one chord is 16 cm, then the length of the other is :a)23 cmb)30 cmc)15 cmd)none of theseCorrect answer is option 'B'. Can you explain this answer?
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