Circles

Question 0

What is the theorem about right angles inscribed in a circle?

Answer 0

If a right triangle is inscribed in a circle, then the hypotenuse is a diameter of the circle.

Question 1

What is the standard equation of a circle?

Answer 1

(x-h)^2 + (y-k)^2 = r^2

Question 2

What is the theorem about tangent segments?

Answer 2

Tangent segments from a common external point are congruent.

Question 3

What is the Arc Addition Postulate?

Answer 3

The measure of an arc formed by two adjacent arcs is the sum of the measures of the two arcs.

Question 4

What is the theorem about diameters being perpendicular?

Answer 4

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc.

Question 5

What is the converse of the right triangle theorem?

Answer 5

If one side of an inscribed triangle is a diameter of the circle, then the triangle is a right triangle and the angle opposite the diameter is a right angle.

Question 6

What is the Measure of an Inscribed Angle Theorem?

Answer 6

The measure of an inscribed angle is one half the measure of its intercepted arc.

Question 7

What is the theorem about two inscribed angles?

Answer 7

If two inscribed angles of a circle intercept the same arc, then the angles are congruent.

Question 8

What is the theorem about chords being a perpendicular bisector?

Answer 8

If one chord is a perpendicular bisector of another chord, then the first chord is a diameter.

Question 8

What is the Angles Inside the Circle Theorem?

Answer 8

If two chords intersect inside circle, then the measure of each angle is one half the sum of the measure of the arcs intercepted by the angle and its vertical angle.

Question 9

What is the theorem about tangent lines and radii?

Answer 9

In a plane, a line is tangent to a circle if the line is perpendicular to a radius of the circle at its endpoint on the circle.

Question 9

What is the Segments of Secants Theorem?

Answer 9

If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the length of the other secant segment and its external segment.

Question 12

What is the theorem about minor arcs and chords?

Answer 12

In the same circle, or in congruent circles, two minor arcs are congruent if their corresponding chords are congruent.

Question 13

What is the theorem about chords being congruent?

Answer 13

In the same circle, or in congruent circles, two chords are congruent if they are equidistant from the center.

Question 15

What is the Quadratic Formula?

Answer 15

x = b+ or - √b^2-4ac
——————–
2a

Question 16

What is the theorem about a tangent and a chord intersecting?

Answer 16

If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc.

Question 17

What is the Angles Outside the Circle Theorem?

Answer 17

If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs.

Question 19

What is the Segments of Secants and Tangents Theorem?

Answer 19

If a secant segment and a tangent segment share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segment equals the square of the length of the tangent segment.

Question 20

What is the theorem about quadrilaterals inscribed in circles?

Answer 20

A quadrilateral can be inscribed in a circle if its opposite angles are supplementary.

Question 21

How do you find the length of a radius?

Answer 21

r=√(x-h)^2 + (y-k)^2

Question 22

What is the Segments of Chords Theorem?

Answer 22

If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.