Circle Geometry Angle Relationships

The video tutorial by Mr. N covers angle relationships in circles, building on previous lessons. It explains the tangent and intersected chord theorem, intersecting lines in circles, and secant and tangent intersections. The video provides formulas for calculating angles based on these relationships and includes problem-solving examples to reinforce understanding.

What is the main focus of the 10-5 lesson?

• Perpendicular lines and angles

• Parallel lines and angles

• Angle relationships in triangles

• Angle relationships in circles

According to the Tangent and Intersected Chord Theorem, if a tangent and a chord intersect at a point on a circle, the measure of each angle formed is:

• The same as the measure of the chord

• Twice the measure of the intercepted arc

• Equal to the measure of the intercepted arc

• Half the measure of the intercepted arc

When two lines intersect inside a circle, the measure of the angle formed is:

• Equal to the smaller intercepted arc

• Equal to the larger intercepted arc

• Half the sum of the intercepted arcs

• Half the difference of the intercepted arcs

If two lines intersect outside a circle, the measure of the angle formed is:

• Half the sum of the intercepted arcs

• Equal to the smaller intercepted arc

• Half the difference of the intercepted arcs

• Equal to the larger intercepted arc

What is a circumscribed angle?

• An angle whose sides are tangents to a circle

• An angle whose sides are chords of a circle

• An angle whose vertex is at the center of a circle

• An angle whose vertex is on the circle

In a circumscribed angle, the measure of the angle is:

• Equal to the measure of the opposite angle

• Twice the measure of the opposite angle

• Half the measure of the opposite angle

• 180 degrees minus the measure of the opposite angle

If a point is on the circle, the measure of the angle is:

• Equal to the intercepted arc

• The same as the intercepted arc

• Twice the intercepted arc

• Half the intercepted arc

In the practice problem, if angle ABC is 70 degrees, what is the measure of arc AB?

• 210 degrees

• 140 degrees

• 70 degrees

• 35 degrees

When solving for x in a circle problem, if the lines intersect inside the circle, you should:

• Add the arcs and divide by two

• Divide the arcs

• Subtract the arcs and divide by two

• Multiply the arcs