Geometry and Trigonometry in Semicircles

What is the radius of the semicircle described in the problem?

• 5 units

• 7 units

• 4 units

• 6 units

What is the measure of each angle formed at the center of the semicircle?

• 40 degrees

• 50 degrees

• 30 degrees

• 20 degrees

Which trigonometric function is used to find the base of triangle OFC?

• Sine

• Cosine

• Secant

• Tangent

What is the length of the base OF in triangle OFC?

• 6 units

• 3 units

• 3√3 units

• 6√3 units

What is the height of triangle OFC?

• 2 units

• 3 units

• 4 units

• 5 units

What is the formula used to calculate the area of a sector?

• Theta/90 * πr²

• Theta/45 * πr²

• Theta/180 * πr²

• Theta/360 * πr²

What is the area of sector COB?

• 5π

• 2π

• 3π

• 4π

How does the area of triangle OBE compare to triangle OFC?

• Larger

• Smaller

• Equal

• Cannot be determined

What is the final area of the blue region?

• 2π

• 3π

• 4π

• 5π

What is the hypotenuse length of triangles OFC and OBE?

• 4 units

• 5 units

• 6 units

• 7 units