Inscribed Angles and Circle Properties

The video tutorial covers the properties of central and inscribed angles, including their measures and relationships. It explains how inscribed angles that intercept the same arc are congruent and explores the properties of right triangles inscribed in circles. The tutorial applies the inscribed angle theorem to solve geometric problems and discusses congruent angles and similar triangles. It also analyzes regular figures and their inscribed angles, concluding with a proof of tangency for a line to a circle.

What is the relationship between a central angle and its intercepted arc?

• The central angle is unrelated to the intercepted arc.

• The central angle is equal to the intercepted arc.

• The central angle is half the intercepted arc.

• The central angle is twice the intercepted arc.

How does the measure of an inscribed angle compare to its intercepted arc?

• It is half the intercepted arc.

• It is twice the intercepted arc.

• It is equal to the intercepted arc.

• It is unrelated to the intercepted arc.

What can be said about two inscribed angles that intercept the same arc?

• They are unrelated.

• They are congruent.

• They are supplementary.

• They are complementary.

What is true about a right triangle inscribed in a circle?

• The hypotenuse is an arc.

• The hypotenuse is a diameter.

• The hypotenuse is a chord.

• The hypotenuse is a tangent.

How do you find the measure of an inscribed angle given the arc measures?

• Add the arc measures and divide by two.

• Subtract the arc measures and divide by two.

• Take half of the intercepted arc measure.

• Double the intercepted arc measure.

What is the sum of the inscribed angles in a regular pentagram-like shape?

• 180 degrees

• 90 degrees

• 270 degrees

• 360 degrees

What is the measure of each inscribed angle in a regular star with five points?

• 72 degrees

• 54 degrees

• 18 degrees

• 36 degrees

What is the relationship between a tangent and a radius at the point of tangency?

• They are parallel.

• They are unrelated.

• They are perpendicular.

• They are equal.

How can you prove a line is tangent to a circle?

• Show it is parallel to a diameter.

• Show it is perpendicular to a radius at the point of tangency.

• Show it is equal to a radius.

• Show it is a chord.

What happens when two circles intersect at a point?

• The point is a common tangent.

• The point is a tangent.

• The point is a diameter.

• The point is a common chord.