1. 14-2b Tangent Lines to Circles
Proof Geometry

2. Center of Circle
To find the center of the circle through a construction
1) Inscribe a triangle in the circle
2) Construct the perpendicular bisectors of each of the sides of the triangle

3. Circle Center and Chord Theorems:
The Perpendicular from the center of the circle to a chord bisects the chord.
The segment from the center of the circle to the midpoint of a chord is perpendicular to the chord.
The perpendicular bisector of a chord passes through the center of the circle.

4. Circle Center and Chord Theorems:
Sketch out the proof for:
The Perpendicular from the center of the circle to a chord bisects the chord.
1)Create a circle with center P and a chord QR. Let PF be perpendicular to chord QR.
2) Introduce radii PQ and PR.
3) Show the two smaller triangles congruent through HL.

5. Circle Center and Chord Theorems:
Sketch out the proof for:
The segment from the center of the circle to the midpoint of a chord is perpendicular to the chord.
1)Create a circle with center P and a chord QR. Let PF be the bisector of chord QR.
2) Introduce radii PQ and PR.
3) Show the two smaller triangles congruent through SSS.

6. Circle Center and Chord Theorems:
1)Create a circle with center P and a chord QR. Let m be the perpendicular bisector of QR through F.
2) By the perpendicular bisector theorem, any point on m is equidistant from the endpoints.
3) Uniqueness shown through any point equidistant from endpoints is on the perpendicular bisector (Thm 6-4).
Circle Center and Chord Theorems:
Sketch out the proof for:
The perpendicular bisector of a chord passes through the center of the circle.

7. Equidistant Chords Theorem:
In the same circle or in congruent circles, chords are equidistant from the center if and only if they are congruent.

8. Equidistant Chords Theorem:
Show: IF equidistant from the center THEN congruent.

9. Equidistant Chords Theorem:
Show: IF congruent THEN equidistant from the center.

10. Homework
Pg. 457 #16-18 Pg. 461 #1, 5, 8