Geometry Ch 12 - Circles

Question 1

Tangent to a Circle

Answer 1

A line in the plane of the circle that intersects the circle in exactly one point.

Question 2

If a line is tangent to a circle…

Answer 2

…then the line is perpendicular to the radius drawn to the point of tangency.

Question 3

If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle…

Answer 3

… then the line is tangent to the circle.

Question 4

The two segments tangent to a circle from a point outside the circle…

Answer 4

… are congruent.

Question 5

Chord

Answer 5

A segment whose endpoints are on a circle.

Question 6

Within a circle or in congruent circles…

Answer 6

(1) Congruent central angles have congruent chords
(2) Congruent chords have congruent arcs
(3) Congruent arcs have congruent central angles.

Question 7

Within a circle or in congruent circles

Answer 7

(1) Chords equidistant from the center are congruent
(2) Congruent chords are equidistant from the center

Question 8

In a circle, a diameter that is perpendicular to a chord…

Answer 8

… bisects the chord and its arcs.

Question 9

In a circle, a diameter that bisects a chord (that is not a diameter)…

Answer 9

…is perpendicular to the chord.

Question 10

In a circle, the perpendicular bisector of a chord…

Answer 10

… contains the center of the circle.

Question 11

Inscribed Angle

Answer 11

An angle formed by two chords in a circle which have a common endpoint. This common endpoint forms the vertex of the inscribed angle. The other two endpoints define an intercepted arc on the circle. … The minor arc is the smaller of the two arcs, while the major arc is the bigger.

Question 12

Inscribed Angle Theorem

Answer 12

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

Question 13

Corollaries to the Inscribed Angle Theorem

Answer 13

(1) Two inscribed angles that intercept the same arc are congruent.
(2) An angle inscribed in a semicircle is a right angle.
(3) The opposite angles of a quadrilateral inscribed in a circle are supplementary.

Question 14

The measure of an angle formed by a tangent and a chord is…

Answer 14

… half the measure of the intercepted arc.

Question 15

Secant

Answer 15

A line that intersects a circle at two points.

Question 16

The measure of an angle formed by two lines that

Answer 16

(1) intersect inside a circle is half the sum of the measures of the intercepted arcs.
(2) intersect outside a circle is half the difference of the measures of the intercepted arcs.

Question 17

For a given point and circle, the product of the lengths of the two segments from the point to the circle…

Answer 17

… is constant along any line through the point and circle.

Question 18

Standard Equation of a Circle

Answer 18

An equation of a circle with center (h, k) and radius r is (x - h)² + (y - k)² = r²

This is in standard form.

Question 19

Locus

Answer 19

A set of points, all of which meet a stated condition.