Question

A square has two of its vertices on a circle and the other two on the tangent to the circle if the diameter of the circle is 10 determine the side of the square​

Answer 1

Side of square is $5\sqrt{2}$

Step-by-step explanation:

• Here it given that vertices of square lie on circle. We know that each angle of square is 90° as well as it lie on circle. So its diagonal is pass through centre of circle.

• It means diameter of circle is diagonal of square.

• We know relation between side and diagonal of square.

        $\mathbf{Side =\frac{Diagonal}{\sqrt{2}}}$

        $\mathbf{Side =\frac{10}{\sqrt{2}}}$

        On rationalise the denominator, we get

        $\mathbf{Side =\frac{10}{\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}}$

        $\mathbf{Side =\frac{10\sqrt{2}}{2}=5\sqrt{2}}$  This is side of square.

Answer 2

$\huge{\underline{\underline{\bf{Solution}}}}$

$\rule{200}{2}$

$\tt given\begin{cases} \sf{A \: square \: has \: two \: verticies \: on \: a \: circle.} \\ \sf{Diameter \: of \: circle = 10} \end{cases}$

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{To \: Find :}}}}$

We have to find the side of the square.

$\rule{200}{2}$

$\Large{\underline{\underline{\bf{Explanation :}}}}$

Since there is a angle of 90° because of tangent. So, diameter of circle is diagonal of square.

We know the relation between side and diagonal of the square

$\Large{\star{\boxed{\sf{Side = \frac{Diagonal}{\sqrt{2}}}}}}$

___________________[Put Values]

$\sf{→Side = \frac{10}{\sqrt{2}}} \\ \\ \bf{Rationalizing \: the \: denominator} \\ \\ \sf{→Side = \frac{10}{\sqrt{2}} \times \frac{\sqrt{2}}{\sqrt{2}}} \\ \\ \sf{→Side = \frac{\cancel{10}\sqrt{2}}{\cancel{2}}} \\ \\ \sf{Side = 5\sqrt{2}} \\ \\ \Large{\star{\boxed{\sf{Side = 5\sqrt{2}}}}}$