Question

ABCD is a rectangle inscribed in a circle. If AB = 16 cm, BC = 12 cm, find the radius and the area of the shaded part of the circle. [Take π = 3.14].

Answer 1

Given:

• ABCD is a rectangle inscribed in a circle.
• Length AB = 16 cm
• Length BC = 12 cm
• π = 3.14

Step 1: Find the diagonal AC of the rectangle, which will be the diameter of the circle.

Since ABCD is a rectangle, using the Pythagorean theorem:

`AC = sqrt(AB^2 + BC^2)`

= `sqrt(16^2 + 12^2)`

= `sqrt(256 + 144)`

= `sqrt(400)`

= 20 cm

Step 2: Find the radius of the circle.

Radius r = `("Diameter")/2`  

= `(AC)/2`

= `20/2`

= 10 cm

Step 3: Find the area of the circle.

Area of circle = πr² 

= 3.14 × 10²

= 3.14 × 100

= 314 cm²

Step 4: Find the area of the rectangle.

Area of rectangle = AB × BC

= 16 × 12 

= 192 cm²

Step 5: Find the area of the shaded part area of circle outside the rectangle.

Area of shaded part = Area of circle – Area of rectangle

= 314 – 192

= 122 cm²

Radius of the circle is 10 cm.

Area of the shaded part of the circle is 122 cm².