Chord and

Tangent Properties

Chord Properties

C1: Congruent chords in a circle determine congruent central angles.

●

C2: Congruent chords in a circle intercept congruent arcs.

●

Chord Properties

C3: Congruent chords in a circle are equidistant from the center

●

Chord Properties

Remark: Distance from a point to a line is measured along the perpendicular segment

from the point to the line.

C4: The perpendicular from the center to a chord is the perpendicular bisector of the chord.

●

Chord Properties

C5: The perpendicular bisector of a chord passes through the center of the circle

●

Chord Properties

Exercises

1. Chord is 12 cm long. If circle P has a radius of 10 cm., how far is the chord from the center?

AB

2. Find the length of the chord if it is 15 cm from the center of the circle whose radius is 17 cm.

Tangent Conjecture:

A tangent to a circle is perpendicular to the radius drawn to the point of tangency.

●

Tangent Properties

Tangent Segments Conjecture:

Tangent segments to a circle from a point outside the circle are congruent.

●

Tangent Properties