The theorems

Question 1

tangency and perpendicular to radii

Answer 1

If a line is tangent to a circle

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

Question 2

if the line is perpendicular to the radius of the ciircle

Answer 2

If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.

Question 3

if two segments tangent to circle form a point outside the circle,

Answer 3

The two segments tangent to a circle from a point outside the circle are congruent

Question 4

congruent central angles, congruent arcs, congruent chords

Answer 4

conguent central angles have congruent chords

congruent chords have congruent arcs.

congruent arcs have congruenct central angles.

Question 5

equidistant

Answer 5

chords equidistant from the center are congruent

congruent chords are equidistant from the center

Question 6

perpendicular bisector of arc and chord and diameter

Answer 6

in a circle:

• a diameter that is perpendicular to a chord bisects the chord and its arcs.
• a diameter that bisects a chord (not a diameter) is perpendicular to the chord
• the perpendicular bisector of a chord contains the center of the circle

Question 7

inscribed angle them

Answer 7

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

Question 8

corollaries to inscribed angle them

Answer 8

• two inscribed angles that intercept the same arc are congruent
• an angle that intercepts a semi-circle is a right angle
• the opposite angles of a quadrilateral inscribed in a circle are supplementary.

Question 9

tangent and chord and arc

Answer 9

the measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

Question 10

angle measurements of the intercepted arcs

Answer 10

the measure of an angle formed by two lines that

intersect inside a circle is half the sum of the measures of the intercepted arcs m<1=0.5(x+y)

intersect outside a circle is half the difference of the measures of the intercepted arcs. m<1=0.5(x-y)

Question 11

the length of the seacants

Answer 11

For a given point and circle, the product of the lengths of the two segments from the point to the circle is constant along any line through the point and circle

a*b=c*d (inside)

(w+x)w= (y+z)y (outside)

(y+z)y=t^2