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AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, is
- a)2
- b)7
- c)6
- d)3
Correct answer is option 'B'. Can you explain this answer?
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Given information:
- AB = 6 cm
- CD = 8 cm
- Radius of the circle = 5 cm
Calculating the distance between the chords:
- Let's consider the center of the circle as point O.
- Join OA, OB, OC, and OD.
- Since AB and CD are parallel chords, the distance between them is equal to the perpendicular distance between the chords from the center of the circle O.
Calculating the perpendicular distance from O to AB:
- In triangle OAB,
- OA = OB = radius = 5 cm (given)
- AB = 6 cm (given)
- Using Pythagorean theorem:
- (OA)^2 + (AB/2)^2 = (OB)^2
- (5)^2 + (3)^2 = (OB)^2
- 25 + 9 = (OB)^2
- OB = √34 cm
- The perpendicular distance from O to AB = OB = √34 cm
Calculating the perpendicular distance from O to CD:
- In triangle OCD,
- OC = OD = radius = 5 cm (given)
- CD = 8 cm (given)
- Using Pythagorean theorem:
- (OC)^2 + (CD/2)^2 = (OD)^2
- (5)^2 + (4)^2 = (OD)^2
- 25 + 16 = (OD)^2
- OD = √41 cm
- The perpendicular distance from O to CD = OD = √41 cm
Calculating the distance between the chords:
- Distance between the chords = √41 - √34
- ≈ 7 cm
Therefore, the distance between the chords is 7 cm, which corresponds to option B.
- AB = 6 cm
- CD = 8 cm
- Radius of the circle = 5 cm
Calculating the distance between the chords:
- Let's consider the center of the circle as point O.
- Join OA, OB, OC, and OD.
- Since AB and CD are parallel chords, the distance between them is equal to the perpendicular distance between the chords from the center of the circle O.
Calculating the perpendicular distance from O to AB:
- In triangle OAB,
- OA = OB = radius = 5 cm (given)
- AB = 6 cm (given)
- Using Pythagorean theorem:
- (OA)^2 + (AB/2)^2 = (OB)^2
- (5)^2 + (3)^2 = (OB)^2
- 25 + 9 = (OB)^2
- OB = √34 cm
- The perpendicular distance from O to AB = OB = √34 cm
Calculating the perpendicular distance from O to CD:
- In triangle OCD,
- OC = OD = radius = 5 cm (given)
- CD = 8 cm (given)
- Using Pythagorean theorem:
- (OC)^2 + (CD/2)^2 = (OD)^2
- (5)^2 + (4)^2 = (OD)^2
- 25 + 16 = (OD)^2
- OD = √41 cm
- The perpendicular distance from O to CD = OD = √41 cm
Calculating the distance between the chords:
- Distance between the chords = √41 - √34
- ≈ 7 cm
Therefore, the distance between the chords is 7 cm, which corresponds to option B.
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AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer?.
AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer? for SSC CGL 2025 is part of SSC CGL preparation. The Question and answers have been prepared according to the SSC CGL exam syllabus. Information about AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC CGL 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer?.
Solutions for AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC CGL.
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AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer?, a detailed solution for AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of AB and CD are two parallel chords drawn on two opposite sides of their parallel diameter such that AB = 6 cm, CD = 8 cm. If the radius of the circle is 5 cm, the distance between the chords, in cm, isa)2b)7c)6d)3Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an
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