A square fits exactly inside a circle with each of its vertices being on the circumference of the circle. The square has sides of length x cm.
The area of the circle is 56cm squared.
Work out value of x.
Give answer correct to 3 significant figures.

The side of the square is 5.971 cm

Step-by-step explanation:

If the square fits the circle exactly, then its diagonal is equal to the diameter of the circle. Since the side of the square has a length of cm, then it's diagonal have the length of cm. Using the circle's area we can find the diagonal of the square, as shown below:

Since the diameter of the circle is the same as the diagonal of the square, then:

The side of the square is 5.971 cm

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.