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

Question

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. \(2\sqrt{3}\)

A. 1

B.  \sqrt{2}

C. 2

D.  2\sqrt{2}

E.  2\sqrt{3}

Archit3110 · Answer

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

rajatvermaenator · Answer

Please check again , it seems you may have done a calculation error. Answer should be 2√3

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anshkool4u · Answer

Answer is 2√3
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

ScottTargetTestPrep · Answer

Note that the line segment connecting the center of the circle with the closest point on the chord creates a right angle with the chord.

Let the length of the line segment (i.e., the chord in question) be L, the distance between the chord and the center of the circle be D, and the radius of the circle be R. By the Pythagorean theorem, we have:

(L/2)^2 + D^2 = R^2

Here, we are given that D = 1 and R = 2 and we need to determine L:

(L/2)^2 + 1^2 = 2^2

L^2/4 + 1 = 4

L^2/4 = 3

L^2 = 12

L = √12 = √4 x √3 = 2√3

Answer: E

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

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

Prep Toolkit

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