Question

A circle is encrypt in a square and equal triangle of side 4√3 cm is inscribed in that circle the length of the diagonal of a square is​

Answer 1

Answer:

Given :

A circle is inscribed in a square,

An equilateral triangle is inscribed in that circle.

Side of triangle = 4√3cm.

To find :

Length of diagonal of square.

Solution :

We know that side of an equilateral triangle = 4√3 cm.

This triangle is inscribed in a circle, it means this circle has a Circumradius.

The formula to find the Circumradius :

So,

Circumradius r :

As we know that, circle is inscribed in a square,

so now we got the half length of side of that square in the form of Circumradius r.

so,

Side of square, s = 2r

so,

side of square = 8 cm.

Now, according to Pythagoras theorem,

In this case both the sides of square are equal and s = 8 cm,

so

Diagonal of square d :

So,

The diagonal of given square = 8√2 cm.

Step-by-step explanation: