Exploring Circle Theorems and Angle Vertices

The video tutorial explains the concept of vertex angles in relation to a circle. It covers three scenarios: when the vertex is on the circle, inside the circle, and outside the circle. For each case, the video describes how to calculate the angle based on the arcs it intercepts. The inscribed angle on the circle is half the intercepted arc, the angle inside the circle is half the sum of the intercepted arcs, and the angle outside the circle is half the difference of the intercepted arcs.

What are the three positions discussed for the vertex of an angle?

• North of the circle, south of the circle, on the circle

• Left of the circle, right of the circle, center of the circle

• Above the circle, below the circle, within the circle

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

What is the relationship between an inscribed angle and its intercepted arc?

• The angle is equal to the size of the arc

• The angle is one-third the size of the arc

• The angle is twice the size of the arc

• The angle is half the size of the arc

What is the angle size of BCD if the intercepted arc BAD is 140 degrees?

• 35 degrees

• 280 degrees

• 140 degrees

• 70 degrees

Which theorem is applied when the vertex of the angle is on the circle?

• The inscribed angle is one-third the size of the intercepted arc

• The inscribed angle is equal to the intercepted arc

• The inscribed angle is twice the size of the intercepted arc

• The inscribed angle is half the size of the intercepted arc

How do you calculate the angle size for a vertex inside the circle?

• Half the sum of the two arcs

• Difference between the two arcs

• Sum of the two arcs

• Twice the sum of the two arcs

If the arcs KI and JH are 210 and 86 respectively, what is the angle size X inside the circle?

• 103 degrees

• 173 degrees

• 148 degrees

• 296 degrees

What is the correct calculation for the angle size when the vertex is inside the circle and the arcs are 210 and 86?

• 148 degrees

• 296 degrees

• 173 degrees

• 103 degrees

What method is used to find the angle size when the vertex is outside the circle?

• Subtracting the minor arc from the major arc and halving the result

• Adding the major and minor arcs and halving the result

• Multiplying the major and minor arcs

• Dividing the major arc by the minor arc

What is the angle size V when the major arc is 190 and the minor arc is 80?

• 35 degrees

• 75 degrees

• 110 degrees

• 55 degrees

How does the angle size compare when the vertex is inside versus outside the circle?

• Inside is larger than outside

• Outside is larger than inside

• They are the same size

• Cannot be determined without additional information