Understanding Circle and Square Geometry

What is the side length of the square ABCD?

• 5 units

• 6 units

• 4 units

• 3 units

In Method 1, what is the length of the diagonal DB of the square?

• 10√2 units

• 10 units

• 5√2 units

• 5 units

Which theorem is used in Method 1 to find the radius of the blue circle?

• Euclidean algorithm

• Fundamental theorem of calculus

• Binomial theorem

• Pythagorean theorem

What is the approximate value of the radius of the blue circle found using Method 1?

• 0.86 units

• 2.5 units

• 1.5 units

• 3.5 units

In Method 2, what is the length of the diagonal DB of the square?

• 10 units

• 10√2 units

• 5 units

• 5√2 units

What is the purpose of rationalizing the denominator in Method 2?

• To simplify the expression

• To determine the perimeter

• To find the hypotenuse

• To calculate the area

What is the final expression for the radius of the blue circle in Method 2?

• 5 + 5√2

• 5 - 5√2

• 15 + 10√2

• 15 - 10√2

What is the approximate value of the radius of the blue circle found using Method 2?

• 1.5 units

• 0.86 units

• 2.5 units

• 3.5 units

Which point is the center of the blue circle in both methods?

• Point D

• Point A

• Point B

• Point O

What is the relationship between DE, EO, and OB in Method 2?

• DE + EO - OB = DB

• DE - EO + OB = DB

• DE - EO - OB = DB

• DE + EO + OB = DB