Circle Geometry and Angle Relationships

The video covers practice problems from Unit 7 Lesson 3, focusing on geometry concepts such as tangents, diameters, inscribed angles, and congruent chords. It explains how to find lengths using the Pythagorean theorem, determine the closest point on a circle, and evaluate statements about arcs and angles. The video also demonstrates proving congruence of chords and understanding line transformations under a 180-degree rotation.

What is the main focus of Unit 7, Lesson 3 practice problems?

• Algebraic equations

• Probability and statistics

• Tangents and diameters in circles

• Properties of triangles

Why is line BD considered tangent to the circle?

• It is perpendicular to the diameter

• It intersects the circle at exactly one point

• It is parallel to the diameter

• It intersects the circle at two points

What is the measure of angle BCA if the arc from A to B is 180 degrees?

• 45 degrees

• 120 degrees

• 60 degrees

• 90 degrees

How do you calculate the length of segment AB if AC is perpendicular to the circle?

• Using the area of the circle

• Using the Pythagorean theorem

• Using the circumference of the circle

• Using the tangent-secant theorem

What is the length of segment AB if AO is 1.8 and the radius is 1?

• 1.2

• 1.0

• 0.8

• 0.5

Which point on the circle is closest to point P?

• Point D

• Point C

• Point B

• Point A

What is the measure of angle BCA if the arc from A to B is 50 degrees?

• 50 degrees

• 100 degrees

• 25 degrees

• 75 degrees

Which statement is true about the central angle BOA?

• It is half the intercepted arc

• It is equal to the intercepted arc

• It is double the intercepted arc

• It is unrelated to the intercepted arc

Which angles are congruent if chords AC and DB intersect at point E?

• Angle DAE and angle CEB

• All of the above

• Angle DAC and angle DBC

• Angle DEC and angle BEA

How can you prove that chords BC and AD are congruent?

• By proving the triangles they form are congruent

• By using the Pythagorean theorem

• By showing they are parallel

• By measuring their lengths directly