Question

Find the length of a chord of a circle radius
$\sqrt{x { }^{2} } + y {}^{2} )cm \:$
whose distance from the centre of the circle is
$ycm$
​

Answer 1

Answer:

Clearly, centre of triangle , circle and square coincides. (Centroid, incenter of equilateral triangle , orthocenter coincides)

Let a be the length of side of an equilateral triangle.

Area of equilateral triangle A

1

=

4

3

a

2

We have radius of inscribed circle r=

2

3

a×

3

1

=

2

3

a

So, diameter=

3

a

We know that the diameter of the inscribed circle is equal to the diagonal of the square.

So, diagonal of square =

3

a

Let x be the length of side of square.

Length of diagonal of square =x

2

⇒x

2

=

3

a

⇒x=

6

a

Area of square A

2

=x

2

=

6

a

2

Now,

A

2

A

1

=

6

a

2

4

3

a

2

⇒

A

2

A

1

=

2

3

3

solution