Question

there are 2 concentric circles,one big and one small . A square ABCD is inscribed inside the big circle while the same square circumscribes the same circle. the square toches the same circle at points P,Q R and S . Determine the ratio of circumference of big circle to the polygon PQRS



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Answer 1

Ratio of circumference of big circle to polygon PQRS  = π : 2

Step-by-step explanation:

Please find the attached diagram to illustrate the question.

We find that the side of square ABCD = 2a

The line from the centre O bisects the chords AB, BC, CD and DA.

So AP = PB = a. The same applies to the other 3 sides of the square.

Therefore, we find that PQ = QR = RS = SP.

This implies that PQRS is also a square.

Radius of big circle = diagonal of the square APOS = a√2

Circumference of big circle = 2πr =  2π * a√2 -----------------(1)

Radius of small circle = side of the square APOS = a

PSO is a right-angled triangle. So PS = root of (OS +OP) = a√2

We conclude that PQRS is also a square.

Circumference of square with side a√2 = 4*a√2 -----------------(2)

Ratio of circumference of big circle to the polygon PQRS

 = 2π * a√2 : 4a√2

 = π : 2

Answer 2

Answer:

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Explanation:

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