Geometry Review: Mastering Circles and Their Properties

What is a point of tangency?

• The point where a circle and a tangent intersect

• The longest chord in the circle

• The center of the circle

• A line that intersects the circle at two points

How do you verify if a segment is tangent to a circle?

• Using the Pythagorean theorem

• Checking if the segment forms a right angle with the radius

• Both A and C

• By measuring the segment

What does the segment addition postulate state in the context of arcs?

• The sum of two arcs is less than 360 degrees

• The sum of two arcs equals the total arc they form together

• None of the above

• The sum of two arcs equals the length of the circle

If two chords are congruent, what can be said about the arcs they subtend?

• No relationship exists

• The arcs are congruent

• The arcs sum up to 180 degrees

• The arcs are not congruent

What property do inscribed angles that intercept the same arc have?

• They are congruent

• They are supplementary

• They are both obtuse

• They are both acute

How do you find the measure of an angle formed by a tangent and a chord through the circle's center?

• Add 180 to the intercepted arc

• Subtract the intercepted arc from 360

• Multiply the intercepted arc by 2

• Divide the intercepted arc by 2

What is the result of the equation 3x + 9 = 12x + 36 when solving for x?

• x = 3

• x = 4

• x = 2.25

• x = 3.75

How do you graph a circle with a center at (4, -2) and a radius of 6?

• Plot the center and draw a circle with a 6-unit radius

• Plot the center and draw a square around it

• Just plot the center; the radius is irrelevant

• None of the above

What is the standard equation of a circle with center (-2, 3) and radius 7?

• (x - 2)^2 + (y + 3)^2 = 49

• (x - 2)^2 + (y - 3)^2 = 7

• (x + 2)^2 + (y - 3)^2 = 49

• (x + 2)^2 + (y + 3)^2 = 7

What does the segment theorem state when applied to a circle?

• Outer segment equals inner segment

• Outer segment times whole equals outer times whole

• Inner segment times whole equals outer segment squared

• None of the above