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# A line segment joining two points on the circumference of a circle is

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Math Expert
Joined: 02 Sep 2009
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A line segment joining two points on the circumference of a circle is  [#permalink]

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11 Jan 2019, 01:26
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Difficulty:

45% (medium)

Question Stats:

65% (01:54) correct 35% (01:53) wrong based on 44 sessions

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A line segment joining two points on the circumference of a circle is one inch from the center of the circle at its closest point. If the circle has a two–inch radius, what is the length of the line?

A. 1

B. $$\sqrt{2}$$

C. 2

D. $$2\sqrt{2}$$

E. $$2\sqrt{3}$$

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A line segment joining two points on the circumference of a circle is  [#permalink]

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Updated on: 12 Jan 2019, 04:01
1
Bunuel wrote:
A line segment joining two points on the circumference of a circle is one inch from the center of the circle at its closest point. If the circle has a two–inch radius, what is the length of the line?

A. 1

B. $$\sqrt{2}$$

C. 2

D. $$2\sqrt{2}$$

E. $$2\sqrt{3}$$

radius = 2 and line segment is 1 inches away from center which would be the length of altitude on the line segment AB
since OA = OB = 2
the point of where line segment is 1 inches from center is c so triangle AOC: 30:60:90 : 1:sqrt3:2
similarly for triangle OBC CB = sqrt 3
total AC+ CB = 2sqrt 3 IMO E
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Originally posted by Archit3110 on 11 Jan 2019, 03:24.
Last edited by Archit3110 on 12 Jan 2019, 04:01, edited 2 times in total.
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Re: A line segment joining two points on the circumference of a circle is  [#permalink]

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11 Jan 2019, 07:14
Please check again , it seems you may have done a calculation error. Answer should be 2√3

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Re: A line segment joining two points on the circumference of a circle is  [#permalink]

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11 Jan 2019, 11:25
This is because the distance between the line and the centre is 1 inch, the radius of the circle is 2 inch. Since, the shortest distance from the centre of the circle to the line joining two points will be the perpendicular bisector of the line, so we can find the distance between the point on the circumference and the point where the line from centre meets.This is equal to (2^2-1^2)^1/2= √3
So, total length of line= 2*√3
Re: A line segment joining two points on the circumference of a circle is   [#permalink] 11 Jan 2019, 11:25
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