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Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then distance between these chords is
- a)5.5 cm
- b)5 cm
- c)3.5 cm
- d)3 cm
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Two parallel chords of a circle whose diameter is 13 cm are respective...
In the figure, AB and CD are the chord with lengths 5 cm and 12 cm;
In Triangle OPB;
OB = Radius = 13/2 cm, PB = 5/2 cm
∴ OP2 = (13/2)2 – (5/2)2
⇒ OP2 = 169/4 – 25/4
⇒ OP2 = 144/4 = 36
⇒ OP = 6 cm
In Triangle OQD;
OD = Radius = 13/2 cm, QD = 12/2 = 6 cm
∴ OQ2 = (13/2)2 – (6)2
⇒ OQ2 = 169/4 – 36
⇒ OQ2 = 25/4
⇒ OQ = 5/2 cm
∴ Distance between these chords = OP – OQ = 6 – 2.5 = 3.5 cm
Most Upvoted Answer
Two parallel chords of a circle whose diameter is 13 cm are respective...
Given information:
- Diameter of the circle = 13 cm
- Length of the parallel chords = 5 cm and 12 cm
Distance between the chords:
To find the distance between the chords, we need to first determine the distance of each chord from the center of the circle.
Distance of 5 cm chord from the center:
Using the property of a perpendicular bisector, we know that the perpendicular bisector of a chord passes through the center of the circle.
So, the distance of the 5 cm chord from the center = (1/2) * sqrt(diameter^2 - chord length^2)
= (1/2) * sqrt(13^2 - 5^2)
= (1/2) * sqrt(169 - 25)
= (1/2) * sqrt(144)
= 6 cm
Distance of 12 cm chord from the center:
Similarly, the distance of the 12 cm chord from the center = (1/2) * sqrt(13^2 - 12^2)
= (1/2) * sqrt(169 - 144)
= (1/2) * sqrt(25)
= 5 cm
Distance between the chords:
Since both chords are on the same side of the diameter, the distance between them is the difference of their distances from the center.
Distance between the chords = 6 cm - 5 cm = 1 cm
Therefore, the distance between the chords is 1 cm. Hence, option 'C' is correct.
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Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then distance between these chords isa)5.5 cmb)5 cmc)3.5 cmd)3 cmCorrect answer is option 'C'. Can you explain this answer?
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Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then distance between these chords isa)5.5 cmb)5 cmc)3.5 cmd)3 cmCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then distance between these chords isa)5.5 cmb)5 cmc)3.5 cmd)3 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then distance between these chords isa)5.5 cmb)5 cmc)3.5 cmd)3 cmCorrect answer is option 'C'. Can you explain this answer?.
Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then distance between these chords isa)5.5 cmb)5 cmc)3.5 cmd)3 cmCorrect answer is option 'C'. Can you explain this answer? for Defence 2024 is part of Defence preparation. The Question and answers have been prepared according to the Defence exam syllabus. Information about Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then distance between these chords isa)5.5 cmb)5 cmc)3.5 cmd)3 cmCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Defence 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two parallel chords of a circle whose diameter is 13 cm are respectively 5 cm and 12 cm in length. If both the chords are on the same side of the diameter, then distance between these chords isa)5.5 cmb)5 cmc)3.5 cmd)3 cmCorrect answer is option 'C'. Can you explain this answer?.
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