If the points A, B, and C are distinct, are line segments AB and AC th

Question

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 .

DangerPenguin · Answer

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"

bionication · Answer

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.

kinghyts · Answer

Statement 1: A is the midpoint of the line segment BC. 
The midpoint of a line divides the line into 2 equal line segments. Sufficient

Statement 2: Arc BC lies on a particular circle with center A.
This means is that BC is the diameter and AB = BC= radius of the circle. Sufficient

Answer should be D

WoundedTiger · Answer

We Bascially need to know whether |B-A|=|A-C|... or is A mid point of BC... We can have 2 cases here

B and C are same points on the line but we are told that the points are distinct so B and C are different points... So A has to be mid point of BC

We will have B+C/2=A or B+C =2A or B-A=A-C

St 1 says A is mid point...Sufficient

St 2 says Arc BC lies on circle with center A so we have AB and AC as radius and radius of same circle are equal

Ans D

Bunuel · Answer

Official Solution:

The question asks us if we have enough information to determine that  AB  and  AC  are the same length.

Statement 1 tells us that  A  is the midpoint of the line segment  BC . By the definition of midpoint, this information implies that segments  AB  and  AC  are the same length. Statement 1 alone is sufficient to answer the question. The answer is A or D.

Statement 2 tells us that points  B  and  C  are the endpoints of an arc on a particular circle with center  A . Any endpoints of an arc are themselves on the circle. This implies that the line segments  AB  and  AC  are radii of the circle and are therefore equal in length. Statement 2 alone is also sufficient to answer the question.

Answer: D.

rhine29388 · Answer

The question is basically asking us whether length (AB) = length (AC)
Statement 1 tells us point A is midpoint of line segment BC. points lie in the order B---A---C or C---A---B
It means that length (BA) = length (AC) So sufficient
Statement 2 tells us that B and C are endpoints of arc present in a circle with center A.
It means that AB and AC are radius of the circle. we know that radius of a circle are equal in lengths,so length (AB) = length (AC)
so sufficient
correct Answer - D

If the points A, B, and C are distinct, are line segments AB and AC th

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