Question

The following question is accompanied by three statements (I), (II), and (III). You have to determine which statements(s) is/are sufficient/necessary to answer the questions.

A triangle is circumscribed by a circle. What is the perimeter of the triangle?

Statement I. The circumference of the circle is 14π cm.

Statement II. The triangle is an isosceles triangle.

Statement III. The largest side of the triangle is the diameter of the circle.

1. Either statement I and II together or Statement II and III together is sufficient to answer the question.
2. The data in statement I alone is sufficient to answer the question.
3. The data in statement I and II together are sufficient to answer the question.
4. The data in all the statements I, II, and III are not sufficient to answer the question.
5. The data in all statements I, II, and III together are necessary to answer the question.

Answer 1

Correct Answer - Option 5 : The data in all statements I, II, and III together are necessary to answer the question.

Calculation:

For Statement I:

We can conclude, the radius of the circle = 7 cm.

∴ the diameter = 14 cm

Statement I alone is not sufficient to answer the question.

For statement II:

The triangle is an isosceles triangle.

Statement II alone is not sufficient to answer the question.

For statement III:

We can conclude that the largest side of the triangle = 14 cm

It is circumscribed by a circle so it will be a right-angled isosceles triangle.

Statement III alone is not sufficient to answer the question.

But if we combine statements I, II, and III we can find the perimeter.