Understanding Circle Theorems

This video tutorial covers the concepts of chords and theorems in circles, focusing on two main theorems. The first theorem discusses the relationship between congruent chords and congruent arcs, while the second theorem explains the conditions under which a chord is a perpendicular bisector of another chord, making it a diameter. The video includes practice problems to apply these theorems, enhancing understanding through examples and demonstrations.

What does the first theorem about chords and arcs state?

• Two arcs are congruent if their corresponding chords are congruent.

• Two chords are congruent if they are parallel.

• Two arcs are congruent if they are central angles.

• Two chords are congruent if they are diameters.

If arc GH measures 100 degrees, what is the measure of arc IJ?

• 100 degrees

• 150 degrees

• 50 degrees

• 200 degrees

In a circle, if arc IJ is 85 degrees and arc HJ is 120 degrees, what is the measure of arc GI?

• 70 degrees

• 85 degrees

• 120 degrees

• 95 degrees

What does the second theorem state about a chord that is a perpendicular bisector of another chord?

• The first chord is a radius.

• The first chord is a diameter.

• The second chord is a tangent.

• The second chord is a secant.

If a diameter is perpendicular to a chord, what can be said about the chord?

• The chord is bisected.

• The chord is a tangent.

• The chord is a secant.

• The chord is a radius.

If ME is 35 degrees, what is the measure of arc CB?

• 140 degrees

• 105 degrees

• 70 degrees

• 35 degrees

How many degrees are in a semicircle?

• 270 degrees

• 360 degrees

• 90 degrees

• 180 degrees

If BD is a diameter and arc DE is 145 degrees, what is the measure of arc DC?

• 180 degrees

• 35 degrees

• 145 degrees

• 90 degrees

What is the algebraic expression to solve for x if a chord is bisected?

• 5x - 4 = 2x + 9

• x + 5 = 2x - 4

• x - 5 = 2x + 4

• 3x + 4 = 2x - 9

What is the value of x if 5x - 4 = 2x + 9?

• 5

• 7

• 3

• 13/3