Math circle quiz

Tangent theorem #1

A line is tangent to a circle if and only if the line is perpendicular to a radius at the endpoint on the circle.

Tangent theorem #2

Tangent segments that intersect at a common external point are congruent.

What is a chord?

A chord is a segment with both endpoints on a circle

Properties of a chord

• Any chord divides a circle into 2 arcs

• The larger arc is called the major arc

• The smaller arc is called the minor arc

Chord theorem 1

In the same or congruent circles (same radii), two minor arcs are congruent if and only if their corresponding chords are congruent.

Chord theorem 2

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

Chord theorem 3

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

Chord theorem 4

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

Intersecting lines and circles

If two lines intersect a circle, these lines can intersect each other in three possible ways - on, inside, or outside the circle.

On the circle interception

Angle = ½ (intercepted arc)

Inside the circle interception

Angle = ½ sum of intercepted arcs

Outside of the circle interception

Angle = ½ difference of the intercepted arcs

Circle formula/equation

(x-h)² + (y-k)² = r²

What part of the circle formula represents the center of the circle?

(h,k)