# Area of Circle and Triangle Example

- Question:
- In the figure below, ABC is a triangle inscribed in the circle with center O that is on the line AB. If AC = 12, BC = 16,
what is the shadded area of the figure above ? ( R is the radius of the circle and PI = 3.14 )

- Solution:
- Point O is on the line AB and point O is the center of the circle, then AB is a diameter, then angle ACB = 90 degree.
- AB
^{2} = AB^{2} + BC^{2}
- (2R)
^{2} = 12^{2} + 16^{2} = 144 + 256 = 400 = 20^{2}
- so 2R = 20
- R = 10
- Area
_{shade} = Area_{circle}/2 - Area_{triangle}
- = (1/2)pi R
^{2} - (1/2) 12 × 16
- = (1/2)[ 3.14 × 10
^{2} - 12 × 16]
- = (1/2)[ 3.14 × 100 - 12 × 16]
- = (1/2)[314 - 192]
- = 61
- Therefore, the area of shaded is 61.

- Rules used in this example:
- 1. In a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two legs.
- 2. The area of a triangle is equal to one-half the product of the base and the altitude (the base is perpendicular to the altitude).
- 3. An inscribed angle is an angle whose vertex lies on a circle and whose sides are chords. The inscribed angle is 90
^{o} when whose opposite chord is a diameter.
- 4. The area of a circle is equal to the product of the constant (pi) and the square of the length of the radius of the circle.