Question

What will be the length of the square inscribed in a circle of radius 5 cm?

(a) 2.34 cm

(b) 3.45 cm

(c) 5√2 cm

(d) 2.45 cm

This question was addressed to me in an international level competition.

This is a very interesting question from Pythagoras Theorem topic in section Triangles of Mathematics – Class 10

Answer 1

Right option is (c) 5√2 cm

Best explanation: The diagram according to the given data is:

ABCD is a square inscribed in a circle of radius 5 cm.

Now, joining the diagonals of the square we get

The diagonals intersect at E. We know that the diagonals of square are perpendicular to each other.

In ∆AED, using Pythagoras Theorem,

AD^2 = DE^2 + AE^2

DE and EA are the radius of the circle, ∴ DE = EA

AD^2 = 2DE^2

AD^2 = 2 × 5^2 = 2 × 25 = 50

AD^2 = 50

AD^2 = 125

AD = √50 = 5√2 cm