Segment Lengths in Circles

a + b = c + d

ab = cd

ac = bd

ad = bc

$$9x\ =\ 21\cdot27$$

$$27x=9\cdot21$$

$$21x=9\cdot27$$

$$x+27\ =\ 9+21$$

 $18\left(7x+2\right)=20\left(6x+3\right)$ 

 $18\left(6x+3\right)=20\left(7x+2\right)$ 

 $18\cdot20=\left(7x+2\right)\left(6x+3\right)$ 

 $7x+2+18=6x+3+20$ 

 $2\left(13\right)-5$ 

 $2\left(13\right)-5+18$ 

 $2\left(13\right)+1$ 

 $2\left(13\right)+1+14$ 

 $2\left(13\right)-5$ 

 $2\left(13\right)-5+18$ 

 $2\left(13\right)+1$ 

 $2\left(13\right)+1+14$ 

$ab=cd$

$a+b=c+d$

$a\left(a+b\right)=c\left(c+d\right)$

$a\left(c+d\right)=c\left(a+b\right)$

 $9+x=8+19$  

 $9x=8\cdot19$  

 $9\cdot8=19x$  

 $9\left(9+x\right)=8\left(8+19\right)$  

 $8\left(8+3x+4\right)=7\left(7+5x+2\right)$  

 $8\left(3x+4\right)=7\left(5x+2\right)$  

 $8\cdot7=\left(5x+2\right)\left(3x+4\right)$  

 $8+3x+4=7+5x+2$  

$18x=24$

$18x^2=24$

$24^2=18x$

$24^2=18\left(18+x\right)$

 $x^2=27\cdot21$ 

 $x^2=27\left(27+21\right)$ 

 $27^2=21x$ 

 $27^2=21\left(21+x\right)$ 

$$3x^2=9\left(9+16\right)$$

$$\left(3x\right)^2=9\left(16\right)$$

$$\left(3x\right)^2=9\left(9+16\right)$$

$$3x^2=9\left(16\right)^{ }$$