THEOREM 6.16: SEGMENTS OF CHORDS THEOREM If two chords intersect in the interior of a circle,
then the product of the lengths of the segment of one
chord is equal to the product of the lengths of the
segments of the other chord.
EA*EB=EC*ED
EXAMPLE:
EA=X+1
EB=X+3 FORMULA: EA*EB=EC*ED
EC=X+7
ED=X+2
(X+1)*(X+3)=(X+7)*(X+2) SUBSTITUTE
(X^2+3X+X+3)=(X^2+2X+7X+14) USE THE FOIL METHOD TO MULTIPLY
(X^2+4X+3)=(X^2+9X+14) COMBINE LIKE TERMS
0=5X=11 SET ONE SIDE EQUAL TO ZERO BY SUBTRACTING (X^2+4X+3) FROM BOTH SIDES
-11=5X SUBTRACT 11 FROM BOTH SIDES
-11/5=5X/11 DIVIDE BOTH SIDES BY 5
-11/5=X SOLVE
SOLUTION: -11/5 OR -2.2
THEOREM 6.16: SEGMENTS OF CHORDS THEOREM
If two chords intersect in the interior of a circle,
then the product of the lengths of the segment of one
chord is equal to the product of the lengths of the
segments of the other chord.
EXAMPLE:
EA=X+1
EB=X+3 FORMULA: EA*EB=EC*ED
EC=X+7
ED=X+2
(X+1)*(X+3)=(X+7)*(X+2) SUBSTITUTE
(X^2+3X+X+3)=(X^2+2X+7X+14) USE THE FOIL METHOD TO MULTIPLY
(X^2+4X+3)=(X^2+9X+14) COMBINE LIKE TERMS
0=5X=11 SET ONE SIDE EQUAL TO ZERO BY SUBTRACTING (X^2+4X+3) FROM BOTH SIDES
-11=5X SUBTRACT 11 FROM BOTH SIDES
-11/5=5X/11 DIVIDE BOTH SIDES BY 5
-11/5=X SOLVE
SOLUTION: -11/5 OR -2.2
CHECK: SUBSTITION
FIND AB: FIND CD:
AB=(-2.2+1)*(-2.2+3) CD=(-2.2+2)*(-2.2+7)
AB= (-1.2)*(0.8) CD=(0.2)*(4.8)
AB=(-0.96) CD=(-0.96)
http://www.regentsprep.org/Regents/mathb/5A1/CircleAngles.htm