Understanding Tangent Circles and Calculating Areas

What is the radius of the quarter circle in the problem?

• 12 units

• 4 units

• 16 units

• 8 units

What is the relationship between the green circle and the semicircle?

• They are internally tangent

• They are externally tangent

• They are concentric

• They are overlapping

Which principle is used to find the radius of the green circle?

• The principle of tangent lines

• The principle of connecting centers

• The principle of equal radii

• The principle of circle symmetry

What is the distance from point O to D?

• 8 units

• X units

• 32 units

• 16 units

In the triangle AEB, what is the expression for the hypotenuse?

• 16 + X

• 8 - X

• 8 + X

• 16 - X

What is the expression for EB derived from triangle AEB?

• Square root of 64 + 16X

• Square root of 32X

• Square root of 256 - 32X

• Square root of 64 - 16X

What is the expression for EB derived from triangle OEB?

• Square root of 64 + 16X

• Square root of 256 - 32X

• Square root of 32X

• Square root of 128 - 16X

What is the radius of the green circle?

• 6 units

• 2 units

• 8 units

• 4 units

What is the formula for the area of a circle?

• πd^2

• 2πr

• πr^2

• πr

What is the area of the green circle?

• 12π square units

• 8π square units

• 16π square units

• 20π square units