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A chord of length 32 cm is placed inside a circle of radius 20 cm and a point whose distance from the centre of the circle is 13 cm, is marked on the chord. Calculate the lengths of the segment of the chord.
- a)21 cm and 11 cm
- b)19 cm and 13 cm
- c)16 cm each
- d)18 cm and 14 cm
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
A chord of length 32 cm is placed inside a circle ofradius 20 cm and a...
AQ = (16 + 5 = 21) cm and QB = 32 - 21 = 11 cm
Most Upvoted Answer
A chord of length 32 cm is placed inside a circle ofradius 20 cm and a...
Given:
Length of chord = 32 cm
Radius of circle = 20 cm
Distance of point from center of circle = 13 cm
To find:
Lengths of the segments of the chord
Solution:
Let O be the center of the circle and AB be the chord of length 32 cm. Let C be the point on AB such that OC is perpendicular to AB. Let D be the midpoint of AB.
We know that the perpendicular from the center of a circle to a chord bisects the chord. Therefore, OD = 16 cm.
Using the Pythagorean theorem in triangle ODC, we get:
CD^2 + 13^2 = 20^2
CD^2 = 20^2 - 13^2
CD = √(20^2 - 13^2) = √(231) ≈ 15.20
Therefore, the lengths of the segments of the chord are:
AC = AD - CD = 16 - √(231) ≈ 10.80
BC = BD + CD = 16 + √(231) ≈ 21.20
Hence, option A is the correct answer.
Length of chord = 32 cm
Radius of circle = 20 cm
Distance of point from center of circle = 13 cm
To find:
Lengths of the segments of the chord
Solution:
Let O be the center of the circle and AB be the chord of length 32 cm. Let C be the point on AB such that OC is perpendicular to AB. Let D be the midpoint of AB.
We know that the perpendicular from the center of a circle to a chord bisects the chord. Therefore, OD = 16 cm.
Using the Pythagorean theorem in triangle ODC, we get:
CD^2 + 13^2 = 20^2
CD^2 = 20^2 - 13^2
CD = √(20^2 - 13^2) = √(231) ≈ 15.20
Therefore, the lengths of the segments of the chord are:
AC = AD - CD = 16 - √(231) ≈ 10.80
BC = BD + CD = 16 + √(231) ≈ 21.20
Hence, option A is the correct answer.
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A chord of length 32 cm is placed inside a circle ofradius 20 cm and a point whose distance from the centre of the circle is 13 cm, is marked on the chord. Calculate the lengths of the segment of the chord.a)21 cm and 11 cmb)19 cm and 13 cmc)16 cm eachd)18 cm and 14 cmCorrect answer is option 'A'. Can you explain this answer?
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A chord of length 32 cm is placed inside a circle ofradius 20 cm and a point whose distance from the centre of the circle is 13 cm, is marked on the chord. Calculate the lengths of the segment of the chord.a)21 cm and 11 cmb)19 cm and 13 cmc)16 cm eachd)18 cm and 14 cmCorrect answer is option 'A'. Can you explain this answer? for Quant 2025 is part of Quant preparation. The Question and answers have been prepared according to the Quant exam syllabus. Information about A chord of length 32 cm is placed inside a circle ofradius 20 cm and a point whose distance from the centre of the circle is 13 cm, is marked on the chord. Calculate the lengths of the segment of the chord.a)21 cm and 11 cmb)19 cm and 13 cmc)16 cm eachd)18 cm and 14 cmCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Quant 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A chord of length 32 cm is placed inside a circle ofradius 20 cm and a point whose distance from the centre of the circle is 13 cm, is marked on the chord. Calculate the lengths of the segment of the chord.a)21 cm and 11 cmb)19 cm and 13 cmc)16 cm eachd)18 cm and 14 cmCorrect answer is option 'A'. Can you explain this answer?.
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