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Two parallel chords of a circle, of diameter 20 cm lying on the opposite sides of the centre are of lengths 12 cm and 16 cm.
The distance between the chords is (SSC CGL 1st Sit. 2013)
The distance between the chords is (SSC CGL 1st Sit. 2013)
- a)16cm
- b)24cm
- c)14 cm
- d)20 cm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two parallel chords of a circle, of diameter 20 cm lying on the opposi...
OA = OC = 10 cm (radius)
AB = 12 cm
AP = PB = 6 cm
CD = 16 cm
CQ = QD = 8 cm
Most Upvoted Answer
Two parallel chords of a circle, of diameter 20 cm lying on the opposi...
Given information:
- Diameter of the circle = 20 cm
- Length of one chord = 12 cm
- Length of another chord = 16 cm
Approach:
To find the distance between the chords, we need to find the height of the trapezium formed by the chords.
Solution:
Step 1: Finding the radius of the circle
The diameter of the circle is given as 20 cm. The radius of the circle is half of the diameter.
Radius = Diameter/2 = 20/2 = 10 cm
Step 2: Finding the distance of each chord from the center of the circle
The distance of each chord from the center of the circle is equal to the perpendicular distance of the chord from the center.
Using the Pythagorean theorem, we can find this distance.
For the chord of length 12 cm:
Distance = √(r^2 - (l/2)^2) = √(10^2 - (12/2)^2) = √(100 - 36) = √64 = 8 cm
For the chord of length 16 cm:
Distance = √(r^2 - (l/2)^2) = √(10^2 - (16/2)^2) = √(100 - 64) = √36 = 6 cm
Step 3: Finding the height of the trapezium
The height of the trapezium is the difference between the distances of the chords from the center.
Height = Distance of longer chord - Distance of shorter chord = 8 - 6 = 2 cm
Therefore, the distance between the chords is 2 cm, which is not one of the given options. Hence, none of the provided options is correct.
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