Circle Properties and Missing Values

Solution Preview

See attached file for formatted solution.

Solve problems and justify arguments about chords and lines tangent to circles

Let's take a quick review on a few parts of a circle.
Circle
The locus of a point, which moves such that its distance from a fixed point always a constant.

The fixed point is called its center and the constant distance is called its radius.
The boundary of the circle is called its circumference.

Chord
A line segment whose end points lie on the circumference of the circle is called a chord.
AB is the chord.

Let's review the properties related to the chord.
Property 1:
In a circle, chords equidistant from the center are congruent.

Property 2:
In a circle, congruent chords are equidistant from the center.

Property 3:
A perpendicular line drawn from the center of a circle to a chord bisects the chord.

Property 4:
The line joining the center and the midpoint of a chord is perpendicular to the chord.

Tangent
A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point.
The line m is called the tangent line.

Point of tangency
The point where a circle and a tangent intersect is the point of tangency.
The point A is called the point of tangency
.
Now let's review the properties related to ...