Properties of Chords and Diameters

The video tutorial covers the geometric concepts of circles, focusing on diameters, chords, and perpendicularity. It explains how a diameter bisects a chord when perpendicular, and how this relates to equal arcs. The tutorial also discusses the converse of these properties and their applications, such as using the Pythagorean theorem in right triangles formed by these geometric properties.

What is the term for a line segment that passes through the center of a circle and has its endpoints on the circle?

• Chord

• Diameter

• Tangent

• Radius

If a chord passes through the center of a circle, what is it called?

• Tangent

• Diameter

• Radius

• Secant

What happens when a chord is perpendicular to a diameter?

• It becomes a radius

• It becomes a tangent

• It bisects the diameter

• It is bisected by the diameter

When a diameter bisects a chord, what can be said about the two segments of the chord?

• They are equal

• They are parallel

• They are tangents

• They are perpendicular

If a chord is bisected by a diameter, and one segment is 3x - 14, what equation can be set up to find x if the other segment is 5x + 2?

• 3x = 5x

• 3x - 14 = 5x + 2

• 3x + 14 = 5x - 2

• 3x - 14 = 2x + 5

What additional property is true for a chord that is perpendicular to a diameter?

• It forms a right angle with the circle

• It is a radius

• It creates two equal arcs

• It is a tangent

If two arcs are equal, what can be inferred about the chord that bisects them?

• It is a tangent

• It is perpendicular to the diameter

• It is a radius

• It is a secant

What is the converse of the perpendicular chord theorem?

• If a chord is bisected, it is perpendicular to the diameter

• If a chord is a diameter, it is perpendicular

• If arcs are unequal, the chord is not bisected

• If a chord is a tangent, it is bisected

How can the perpendicular chord theorem be used in problem-solving?

• To apply the Pythagorean theorem

• To find the tangent

• To determine congruent arcs

• To find the radius