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In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is
(2018)
- a)√13
- b)√14
- c)√11
- d)√12
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In a circle, two parallel chords on the same side of a diameter have l...
Let the 6 cm long chord be x cm away from the centre of the circle. Let the radius of the circle be r cm. The perpendiculars from the centre of the circle to the chords bisect the chords.
r2 = x2 + 32 = (x + 1)2 + 22
On solving, x = 2 and r = √13
r2 = x2 + 32 = (x + 1)2 + 22
On solving, x = 2 and r = √13
Most Upvoted Answer
In a circle, two parallel chords on the same side of a diameter have l...
Let $O$ be the center of the circle, and let $AB$ and $CD$ be the two parallel chords, with $AB$ closer to the diameter $EF$ than $CD$. Let the distance between $AB$ and $CD$ be $GK$, and let the intersection of $AB$ and $CD$ be $I$.
[asy] size(8cm); pair O = (0,0); draw(Circle(O,1)); dot(O); pair E=dir(180), F=dir(0); dot(E); dot(F); draw(E--F); pair A,E,B,D,C; A=dir(167); dot(A); E=dir(180); dot(E); B=dir(15); dot(B); D=dir(205); dot(D); C=dir(-15); dot(C); draw(A--B); draw(C--D); pair I = extension(A,B,C,D); dot(I); draw(I--O); pair G,K; G=dir(125); dot(G); K=dir(55); dot(K); draw(G--K); dot(E); [/asy]
Let $EO=r$. Then $EB=EO+OB=r+1$, $EA=EB+BA=EB+CD=r+1+4=r+5$, and $EI^2=EA^2-AI^2=(r+5)^2-3^2=r^2+10r+16$. Since $EI=IK=1$, we have
\[r^2+10r+16=1.\]
\[r^2+10r+15=0\]
\[(r+5)(r+3)=0.\]
Because the radius of a circle must be positive, we have $r=\boxed{-3}$.
[asy] size(8cm); pair O = (0,0); draw(Circle(O,1)); dot(O); pair E=dir(180), F=dir(0); dot(E); dot(F); draw(E--F); pair A,E,B,D,C; A=dir(167); dot(A); E=dir(180); dot(E); B=dir(15); dot(B); D=dir(205); dot(D); C=dir(-15); dot(C); draw(A--B); draw(C--D); pair I = extension(A,B,C,D); dot(I); draw(I--O); pair G,K; G=dir(125); dot(G); K=dir(55); dot(K); draw(G--K); dot(E); [/asy]
Let $EO=r$. Then $EB=EO+OB=r+1$, $EA=EB+BA=EB+CD=r+1+4=r+5$, and $EI^2=EA^2-AI^2=(r+5)^2-3^2=r^2+10r+16$. Since $EI=IK=1$, we have
\[r^2+10r+16=1.\]
\[r^2+10r+15=0\]
\[(r+5)(r+3)=0.\]
Because the radius of a circle must be positive, we have $r=\boxed{-3}$.
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In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is(2018)a)√13b)√14c)√11d)√12Correct answer is option 'A'. Can you explain this answer?
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In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is(2018)a)√13b)√14c)√11d)√12Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is(2018)a)√13b)√14c)√11d)√12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is(2018)a)√13b)√14c)√11d)√12Correct answer is option 'A'. Can you explain this answer?.
In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is(2018)a)√13b)√14c)√11d)√12Correct answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is(2018)a)√13b)√14c)√11d)√12Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In a circle, two parallel chords on the same side of a diameter have lengths 4 cm and 6 cm. If the distance between these chords is 1 cm, then the radius of the circle, in cm, is(2018)a)√13b)√14c)√11d)√12Correct answer is option 'A'. Can you explain this answer?.
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