Multiple choice

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?

  1. Only I

  2. Only II

  3. both I and II

  4. neither I nor II
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

I: Square side 10, diagonal = 10*sqrt(2). If inscribed in a circle, diagonal is diameter, so radius = 5*sqrt(2). Correct. II: Circle inscribed in square side 10, diameter = 10, radius = 5. Correct.

AI explanation

For a square of side 10 inscribed in a circle, the circle's radius is half the square's diagonal, so the radius is 10 times the square root of 2 divided by 2, which equals 5 times the square root of 2. When a circle is inscribed in a square of side 10, its diameter equals the side of the square, making the radius 10 divided by 2, which is 5. Both statements I and II apply the correct geometric properties and yield the right values.

Keep practicing — related questions