Circle Theorems and Radical Simplification

This video tutorial demonstrates how to use chord properties and the Pythagorean theorem to find the distance from a chord to the center of a circle. The problem involves a circle with a diameter of 60 cm and a chord of 20 cm. By drawing the circle and applying the Pythagorean theorem, the distance is calculated and simplified to 20√2 cm. Key concepts include drawing radii, using perpendicular bisectors, and simplifying radicals.

What is the diameter of the circle mentioned in the problem?

• 30 cm

• 40 cm

• 50 cm

• 60 cm

What is the length of the chord in the circle?

• 40 cm

• 30 cm

• 20 cm

• 10 cm

What is the first step in solving the problem after identifying the circle's diameter and chord?

• Draw the chord perpendicular to the diameter

• Calculate the area of the circle

• Find the circumference of the circle

• Draw the radius from the center to the chord

Why is it important to draw a radius in this problem?

• To find the circumference

• To identify a right triangle

• To measure the diameter

• To calculate the area

What theorem is used to find the distance from the center to the chord?

• Theorem of Circle Areas

• Pythagorean Theorem

• Chord Length Theorem

• Diameter Theorem

What is the hypotenuse in the right triangle formed in the problem?

• The chord

• The distance from the center to the chord

• The radius

• The diameter

What is the length of each half of the chord after it is bisected?

• 20 cm

• 5 cm

• 10 cm

• 15 cm

What is the equation used to apply the Pythagorean theorem in this problem?

• a^2 + b^2 = c^2

• c^2 = a^2 + b^2

• a^2 = b^2 + c^2

• b^2 = a^2 + c^2

What is the value of the radius used in the Pythagorean theorem?

• 40 cm

• 10 cm

• 20 cm

• 30 cm

What is the value of the half-chord used in the Pythagorean theorem?

• 15 cm

• 5 cm

• 20 cm

• 10 cm