1. Products of Intercepts

2. Products of Intercepts
D
B
X
A
C

3. Products of Intercepts
D
B
AX  BX  CX  DX
X
A
C

4. Products of Intercepts
D
B
AX  BX  CX  DX
X product of intercepts of intersecting chords
A
C

5. Products of Intercepts
D
B
AX  BX  CX  DX
X product of intercepts of intersecting chords
A
C
“endpoint of the chord to the point of intersection (AX) times endpoint
of the chord to the point of intersection (BX) equals endpoint of the
chord to the point of intersection (CX) times endpoint of the chord to
the point of intersection (DX)

6. X
B
C
A
D

7. Note: secants intersect outside the circle
X
B
C
A
D

8. Note: secants intersect outside the circle
X
B
AX  BX  CX  DX
C
A
D

9. Note: secants intersect outside the circle
X
B
AX  BX  CX  DX
A
C
product of intercepts of intersecting secants
D

10. Note: secants intersect outside the circle
X
B
AX  BX  CX  DX
A
C
product of intercepts of intersecting secants
D
A
X
C
D

11. Note: secants intersect outside the circle
X
B
AX  BX  CX  DX
A
C
product of intercepts of intersecting secants
D
A
X
AX 2  CX  DX
C
D

12. Note: secants intersect outside the circle
X
B
AX  BX  CX  DX
A
C
product of intercepts of intersecting secants
D
A
X
AX 2  CX  DX
C
square of tangents  product of intercepts
D

13. Note: secants intersect outside the circle
X
B
AX  BX  CX  DX
A
C
product of intercepts of intersecting secants
D
Exercise 9G; 1ace, 2, 4, 6, 9a
A
X
AX 2  CX  DX
C
square of tangents  product of intercepts
D