Item contains a Question followed by two Statements. Answer each item using the following instructions : 

Question: Can a circle be drawn through the points A, B and C ?

Statement I: AB = 5 cm, BC = 5 cm, CA = 6 cm.  

Statement II: AB = 3 cm, BC = 4 cm, CA = 7 cm. 

Concept:

The sum of the length of the two sides of a triangle is greater than the length of the third side.

Explanation:

Let's first check whether these points can form a triangle or not (i.e. collinear point).

Statement:1  AB = 5 cm, BC = 5 cm, CA = 6 cm

5 + 5 > 6

5 + 6 > 5

So, A, B & C can form the tirangle.

Therefore, the circle can be drawn from these points.

Statement:2  AB = 3 cm, BC = 4 cm, CA = 7 cm. 

3 + 4 = 7

So A, B & C are collinear points & a circle can not be drawn.

Clearly, we can see, we are able to answer the given question with Statement I but not with Statement II.

∴ The correct answer will be option A.

Alternate MethodConcepts or formulas:

A circle can be drawn through three points if they form a triangle, and the sum of any two sides must be greater than the third side (Triangle Inequality Theorem).
Calculation steps:

Statement I:
⇒ 5 cm + 5 cm > 6 cm (True)
⇒ 5 cm + 6 cm > 5 cm (True)
⇒ 6 cm + 5 cm > 5 cm (True)

All inequalities hold; hence, a circle can be drawn.
Statement II:
⇒ 3 cm + 4 cm > 7 cm (False)

The inequality does not hold; hence, a circle cannot be drawn.
Conclusion:

From Statement I, a circle can be drawn. Statement II fails to satisfy the triangle inequality.
Therefore, the correct answer is: 1) Choose this option if the Question can be answered by one of the Statements alone but not by the other.