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805+ (Hard)|   Geometry|      
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nick1816
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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches Updated on: 10 Jun 2019, 10:20
Originally posted by nick1816 on 10 Jun 2019, 02:47.
Last edited by nick1816 on 10 Jun 2019, 10:20, edited 1 time in total.
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Difficulty:

95% (hard)

Question Stats:

35% (02:24) correct 65% (02:02) wrong based on 130 sessions

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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the arc AB at E. What is the radius of the circle?

1. AB is not a diameter of the circle.
2. The distance between AB and the tangent at E is 5 cm.
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B
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chetan2u
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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches 10 Jun 2019, 08:56
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nick1816
AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle?

1. AB is not a diameter of the circle.
2. The distance between AB and the tangent at E is 5 cm.
Show more


Statement 1 does not mean much..

2. The distance between AB and the tangent at E is 5 cm


We can draw a triangle by joining E with the center. This line OE will bisect chord AB at 90'.
The triangle AOG will give a value of r ..
\(r^2=(r-5)^2+2.5^2......r^2=r^2+25-10r+6.25.....10r=31.25....r=3.125\)

Although B is s the answer, but values are not proper as we get r-5 a negative quantity.
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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches 10 Jun 2019, 09:56
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chetan2u
nick1816
AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle?

1. AB is not a diameter of the circle.
2. The distance between AB and the tangent at E is 5 cm.


Statement 1 does not mean much..

2. The distance between AB and the tangent at E is 5 cm


We can draw a triangle by joining E with the center. This line OE will bisect chord AB at 90'.
The triangle AOG will give a value of r ..
\(r^2=(r-5)^2+2.5^2......r^2=r^2+25-10r+6.25.....10r=31.25....r=3.125\)

Although B is s the answer, but values are not proper as we get r-5 a negative quantity.
Show more

But , the length can't be in negative , right.? And hence, the answer should be E. Correct me if am wrong.

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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches 10 Jun 2019, 10:15
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I've edited the question, now it make sense LOL!!
AO=OB=OE=r
ED=5
DO=5-r

\((5-r)^2+(2.5)^2=r^2\)
r=3.125

(5-r) is positive


chetan2u
nick1816
AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches the minor arc AB at E. What is the radius of the circle?

1. AB is not a diameter of the circle.
2. The distance between AB and the tangent at E is 5 cm.


Statement 1 does not mean much..

2. The distance between AB and the tangent at E is 5 cm


We can draw a triangle by joining E with the center. This line OE will bisect chord AB at 90'.
The triangle AOG will give a value of r ..
\(r^2=(r-5)^2+2.5^2......r^2=r^2+25-10r+6.25.....10r=31.25....r=3.125\)

Although B is s the answer, but values are not proper as we get r-5 a negative quantity.
Show more

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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches 07 Jul 2020, 23:07
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Why is stetment one not needed. If one is true the reaius will be 2.5 . Is it because in the stem minor arc has been mentioned, implying that AB is not a diameter
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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches 09 Jul 2020, 02:47
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Is it right to assume that the tangent is drawn on minor axis? If it was on major axis AB, then the radius would have been different

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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches 10 Jul 2020, 19:36
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Hi chetan2u ,
The question has been modified. Now the stem does not mention intersection on either minor or major arc. I feel it should be C now. Could you please revisit this question ?


Regards

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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches 11 Jul 2020, 04:10
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ShubhamG
Is it right to assume that the tangent is drawn on minor axis? If it was on major axis AB, then the radius would have been different

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Actually not, even if the tangent is on the major arc, then also it would be the same. Please see attached to find the solution -
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AB is a chord of a circle. AB = 5 cm. A tangent parallel to AB touches 22 Jul 2020, 10:10
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Do I actually need to calculate the radius to know that statement 2 is enough? Doesn't fixing three points of a circle (by means of relative distances of point E, A, and B) automatically fix the radius of the circle?

Can anyone let me know if my reasoning is flawed?
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