Understanding Circle Circumference and Right Triangles

The video tutorial explains how to determine the circumference of a circle using given information. It starts by introducing the formula for circumference and then discusses the properties of circle segments and chords. The tutorial forms a right triangle using these segments and applies the Pythagorean theorem to find the radius. Finally, it calculates the circumference using the derived radius and provides a decimal approximation.

What is the formula for the circumference of a circle in terms of its diameter?

• C = πr²

• C = 2πr

• C = 2d

• C = πd

In the given geometric setup, what is the significance of the perpendicular bisector of the chord?

• It forms an equilateral triangle.

• It divides the circle into two equal halves.

• It is parallel to the diameter.

• It bisects the chord into two equal segments.

Which theorem is used to find the radius of the circle in this problem?

• The Law of Sines

• The Pythagorean Theorem

• The Triangle Inequality Theorem

• The Law of Cosines

If one leg of the right triangle is 3 cm and the other is 4.5 cm, what is the length of the hypotenuse?

• 6 cm

• √29.25 cm

• 5.5 cm

• 5 cm

Why is only the positive solution for the radius considered?

• Because the radius can be negative

• Because the radius is a length and must be positive

• Because the positive solution is easier to calculate

• Because the negative solution is incorrect

What is the next step after finding the radius to calculate the circumference?

• Divide the radius by 2

• Square the radius

• Multiply the radius by π

• Use the formula C = 2πr

How is the circumference rounded in this problem?

• To the nearest integer

• To the nearest hundredth

• To the nearest tenth

• To the nearest thousandth

What is the approximate value of the circumference calculated in this problem?

• 32.98 cm

• 33.98 cm

• 35.98 cm

• 34.98 cm

What is the role of the calculator in the final steps of the problem?

• To verify the radius

• To approximate the circumference

• To find the diameter

• To check the angle measures

What is the unit of the final circumference value?

• Meters

• Millimeters

• Centimeters

• Inches