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# 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.