Question

I) lf a square of side $10$ is inscribed in a circle, then the radius of the circle is $5$ $\sqrt{2}$
II) lf a circle is inscribed in a square of side $10$ so that the circle touches the $4$ sides internally, then radius is $5$.
Which of above statements is true?

• A. Only I
• B. Only II
• C. both I and II
• D. neither I nor II

Answer 1

Answer: (C)

both I and II

ABCD is a square inscribed in a cirde
then$\angle DAB={90}^0$
then DB is a diameter of circle
Let $a$ is & side of square ABCD
$\therefore$ $DB=\sqrt{2}a$
so, Given $a=10$
$\therefore$ diasmeter of circle $=\sqrt{2}a=10\sqrt{2}$
radius=$5\sqrt{2}$ true
Let, ABCD is a square of side $10$
and circle is inscribed in square
as we sec, AE and AF are tangents to circle
$\therefore$AE=AF=DH=HC=CG=BG=BE=$\frac{10}{2}=5$
$\therefore$radius of circle is $5$.