Question

the circumference of a circle is 132 cm find the side of a square inscribed in the circle

Answer 1

This ur answer. hope u got the answer

Answer 2

Given data:-

• The circumference of a circle is 132 cm

Solution:-

Let, quadrilateral ABCD is a inscribed square.

{We need to find radius ( r ) of circle}

→ Perimeter of circle = 2πr

{From given}

→ 132 = 2 × 22/7 × r

→ 132 = 44/7 × r i.e.

→ r = {132 × 7}/44

→ r = 924/44

→ r = 175/44

→ r = 21 cm

According to figure AC is diameter.

AO & OC are radius of circle.

We know,

→ Diameter = 2 × radius

→ Diameter = 2 × 21

→ Diameter = 42 cm

::Properties of square::

• All side of square are equal in length.
• All angle of square are equal to 90° or they are called as right angle
• Diameter = 21 cm of circle is know to be hypotenuse of square according to fingure and Properties of square.
• According to property we can assime that → DC = BC = x

Now, we use pythagoras theorem to find side of square.

So, now from figure

→ (AD)² = (DC)² + (BC)²

→ (42)² = (x)² + (x)²

→ 1764 = 2x² i.e.

→ x² = 1764/2

→ x² = 882

→ x = √882 cm

→ x = 21√2 cm

Hence, the length of side of square is 21√2 cm.

{Note:- 21√2cm = 29.69848481 cm}