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If a point C lies between two points A and B such that AC = BC, then AB is equal to
  • a)
    2AC
  • b)
    3AC
  • c)
    4AC
  • d)
    AC
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If a point C lies between two points A and B such that AC = BC, then A...
In figure, point C is between A and B.

[Things which coincide with one another are equal]
∴ AC + CB = AB [Given]
But AC = BC
∴ AC + AC = AB
⇒ 2AC = AB
⇒ AB = 2AC
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Community Answer
If a point C lies between two points A and B such that AC = BC, then A...
Explanation:

When a point C lies between two points A and B such that AC = BC, it means that point C is equidistant from both points A and B. In other words, point C is the midpoint of the line segment AB.

To prove that AB is equal to 2 times AC, we can use the concept of the midpoint.

Proof:

Let's assume that point C is the midpoint of the line segment AB.

We know that AC = BC (given).
Let's consider AC as x. So, BC will also be x.

Since C is the midpoint of AB, we can say that AC = CB = x.

Using the concept of the midpoint, we can say that the distance between A and C is equal to the distance between C and B.

So, AC + CB = AB

Substituting the values of AC and CB, we get:
x + x = AB
2x = AB

Therefore, AB is equal to 2 times AC.

Hence, the correct answer is option 'A'.
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