Circle Geometry and Angle Relationships

This video tutorial explains the angles inside the circle theorem, focusing on the scenario where two chords intersect inside a circle. It details how to calculate the measure of angles formed by these intersecting chords using the intercepted arcs. The video provides two examples: one where the angle is calculated using given arc measures, and another where the value of x is determined using supplementary angles.

What are the three possible ways two lines can intersect a circle?

• On the circle, inside the circle, outside the circle

• On the circle, tangent to the circle, parallel to the circle

• Inside the circle, tangent to the circle, parallel to the circle

• Outside the circle, tangent to the circle, parallel to the circle

What does the theorem state about the measure of angles formed by intersecting chords inside a circle?

• It is equal to the sum of the intercepted arcs

• It is equal to the difference of the intercepted arcs

• It is half the sum of the intercepted arcs

• It is double the sum of the intercepted arcs

How do you calculate the measure of angle one using the theorem?

• Add the intercepted arcs and multiply by two

• Subtract the intercepted arcs and divide by two

• Add the intercepted arcs and divide by two

• Subtract the intercepted arcs and multiply by two

Which arcs are used to calculate the measure of angle one?

• Arc AC and Arc BD

• Arc AB and Arc CD

• Arc DC and Arc AB

• Arc AD and Arc BC

How do you calculate the measure of angle two using the theorem?

• Add the intercepted arcs and multiply by two

• Subtract the intercepted arcs and divide by two

• Add the intercepted arcs and divide by two

• Subtract the intercepted arcs and multiply by two

Which arcs are used to calculate the measure of angle two?

• Arc AC and Arc BD

• Arc DC and Arc AB

• Arc AD and Arc BC

• Arc AB and Arc CD

In Example Problem 1, what is the measure of arc BD?

• 92 degrees

• 143 degrees

• 156 degrees

• 130 degrees

In Example Problem 1, what is the measure of arc AC?

• 156 degrees

• 130 degrees

• 92 degrees

• 143 degrees

What is the value of x in Example Problem 1?

• 92 degrees

• 143 degrees

• 156 degrees

• 130 degrees

In Example Problem 2, what is the measure of the given angle?

• 94 degrees

• 86 degrees

• 80 degrees

• 92 degrees