Postulates & Theorems - chapter 12

Question 1

If a line is tangent to a circle, then it is ….

Answer 1

perpendicular to the radius drawn to the point of tangency. (theo. 12-1-1)

Question 2

If a line is perpendicular to a radius of a circle at a point on the circle, then ….

Answer 2

the line is tangent to the circle. (theo. 12-1-2)

Question 3

If two segments are tangent to a circle from the same external point, then ….

Answer 3

the segments are congruent. (theo. 12-1-3)

Question 4

ARC ADDITION POSTULATE: The measure of an arc formed by two adjacent arcs is ….

Answer 4

the sum of the measures of the two arcs. (post. 12-2-1)

Question 5

In a circle or congruent circles, congruent central angles have …. (a), congruent chords have …. (b), and congruent arcs have …. (c)

Answer 5

(a) congruent chords
(b) congruent arcs
(c) congruent central angles (theo. 12-2-2)

Question 6

In a circle, if a radius (or diameter) is perpendicular to a chord, then ….

Answer 6

it bisects the chord and its arc. (theo. 12-2-3)

Question 7

In a circle, the perpendicular bisector of a chord is ….

Answer 7

a radius (or diameter). (theo.12-2-4)

Question 8

INSCRIBED ANGLE THEOREM: The measure of an inscribed angle is ….

Answer 8

half the measure of its intercepted arc. ((theo. 12-4-1)

Question 9

If inscribed angles of a circle intercept the same arc or are subtended by the same chord or arc, then ….

Answer 9

the angles are congruent. (cor. 12-4-2)

Question 10

An inscribed angle subtends a semicircle if and only if ….

Answer 10

the angle is a right angle. (theo. 12-4-3)

Question 11

If a quadrilateral is inscribed in a circle, then its opposite angles ….

Answer 11

are supplementary. (theo. 12-4-4)

Question 12

If a tangent and a secant (or chord) intersect on a circle at the point of tangency, then the measure of the angle formed is ….

Answer 12

half the measure of its intercepted arc. (theo. 12-5-1)

Question 13

If two secants or chords intersect in the interior of a circle, then the measure of each angle formed is ….

Answer 13

half the sum of the measures of its intercepted arcs. (theo. 12-5-2)

Question 14

If a tangent and a secant, two tangents, or two secants intersect in the exterior of a circle, then the measure of the angle formed is ….

Answer 14

half the difference of the measures of its intercepted arcs. (theo. 12-5-3)

Question 15

CHORD-CHORD PRODUCT THEOREM: If two chords intersect in the interior of a circle, then ….

Answer 15

the products of the lengths of the segments of the chords are equal. (theo. 12-6-1)

Question 16

SECANT-SECANT PRODUCT THEOREM: If two secants intersect in the exterior of a circle, then ….

Answer 16

the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment. (theo. 12-6-2)

Question 17

SECANT-TANGENT PRODUCT THEOREM: If a secant and a tangent intersect in the exterior of a circle, then ….

Answer 17

the product of the lengths of the secant segment and its external segment equals the length of the tangent segment squared. (theo. 12-6-3)

Question 18

EQUATION OF A CIRCLE: The equation of a circle with center (h, k) and radius r is ….

Answer 18

(x - h)^2 + (y - k)^2 = r^2 (theo. 12-7-1)