Chord Lengths and Circle Theorems

The video tutorial explains how to find the radius of a circle when given a chord length and its distance from the center. It starts by drawing the circle and identifying key segments, then uses the Pythagorean theorem to set up an equation. Finally, it solves the equation to determine the radius length.

What is the length of the chord given in the problem?

• 10 cm

• 12 cm

• 14 cm

• 16 cm

How far is the chord from the center of the circle?

• 5 cm

• 4 cm

• 3 cm

• 2 cm

What is the name given to the perpendicular segment from the center to the chord?

• AC

• OB

• AB

• OC

What happens to a chord when a diameter is perpendicular to it?

• It disappears

• It doubles in length

• It is bisected

• It becomes a radius

What is the length of each segment when the chord is bisected?

• 4 cm

• 5 cm

• 6 cm

• 7 cm

Which theorem is used to find the radius of the circle?

• Archimedes' Principle

• Euclid's Theorem

• Pythagorean Theorem

• Thales' Theorem

What is the equation set up using the Pythagorean theorem?

• 5^2 + 7^2 = X^2

• 3^2 + 5^2 = X^2

• 4^2 + 6^2 = X^2

• 6^2 + 8^2 = X^2

What is the simplified form of the square root of 52?

• 4√13

• 3√13

• 2√13

• 5√13

What is the final length of the radius of the circle?

• 2√13 cm

• 4√13 cm

• 3√13 cm

• 2√3 cm