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12 Nov 2014, 10:03
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D
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Difficulty:
5%
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Question Stats:
92% (00:53) correct
8%
(01:40)
wrong
based on 119
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Tough and Tricky questions: Geometry.
If the points \(A\), \(B\), and \(C\) are distinct, are line segments \(AB\) and \(AC\) the same length?
(1) \(A\) is the midpoint of the line segment \(BC\).
(2) Arc \(BC\) lies on a particular circle with center \(A\).
Kudos for a correct solution.
Updated on: 13 Nov 2014, 08:21
Originally posted by DangerPenguin on 12 Nov 2014, 11:15.
Last edited by DangerPenguin on 13 Nov 2014, 08:21, edited 1 time in total.
Last edited by DangerPenguin on 13 Nov 2014, 08:21, edited 1 time in total.
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statement 1: sufficient
If A is the midpoint of BC, then AB must be equal to AC.
statement 2: sufficient
The point from the center of a circle to any point on it's edges is the radius and each circle only has 1 radius so AB must be equal to AC.
Answer D ^_^
edit: meant to say "each circle has only 1 value for radius"
If A is the midpoint of BC, then AB must be equal to AC.
statement 2: sufficient
The point from the center of a circle to any point on it's edges is the radius and each circle only has 1 radius so AB must be equal to AC.
Answer D ^_^
edit: meant to say "each circle has only 1 value for radius"
12 Nov 2014, 11:28
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One a coordinate plane, there are three distinct points in no particular order. A, B, and C.
Statement 1: All line segments have a midpoint that splits the line in half. Line segments BC indicates that points B and C are connected. Point A is the midpoint of this line: B-----A-----C. Therefore, point A splits the line in half, making segments AB and AC equivalent in length.
Statement 2: A circle has an infinite number of radii, all equal in length: from the center to the edge of the circle. If points B and C constitute part of the arc, they lie on the one the edge. It can easily be concluded that points B and Point C are equal to the length of the radii. Therefore, they are equidistant from the center and are equal in length.
Statement 1: All line segments have a midpoint that splits the line in half. Line segments BC indicates that points B and C are connected. Point A is the midpoint of this line: B-----A-----C. Therefore, point A splits the line in half, making segments AB and AC equivalent in length.
Statement 2: A circle has an infinite number of radii, all equal in length: from the center to the edge of the circle. If points B and C constitute part of the arc, they lie on the one the edge. It can easily be concluded that points B and Point C are equal to the length of the radii. Therefore, they are equidistant from the center and are equal in length.
