Question

Given Circle O in Figure 2, find the following:

a. The value of x.
b. The radius of the circle.
c. The circumference of the circle.
d The area of the circle

Answer 1

1. x = 5
2. Radius = 5
3. Circumference = 31.4
4. Area = 78.5

Explanation:

Finding x :

• Applying the Pythagorean Theorem,
• x² + 12² = (8 + x)²
• x² + 144 = 64 + 16x + x²
• 16x = 80
• x = 5

Finding the radius :

• The radius of the circle is equal to x (According to the diagram)
• Radius = 5

Finding the circumference :

• Circumference = 2πr
• Circumference = 2 x 3.14 x 5
• Circumference = 3.14 x 10
• Circumference = 31.4

Finding the area :

• Area = πr²
• Area = 3.14 x (5)²
• Area = 3.14 x 25
• Area = 78.5