Segment Lengths in Circles

Segment Lengths in Circles

Grab some paper and and a pencil!

Segment Lengths

• a and b are parts of one chord

• c and d are parts of another

• To find a missing length when the intersection is INSIDE the circle, use the formula: ab = cd

Multiple Choice

What is the formula for finding segment lengths?

• a + b = c + d

• ab = cd

• ac = bd

• ad = bc

Multiple Choice

Which equation would you use to solve for x?

• $$9x\ =\ 21\cdot27$$

• $$27x=9\cdot21$$

• $$21x=9\cdot27$$

• $$x+27\ =\ 9+21$$

Multiple Choice

Which equation would you use to solve for x?

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

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

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

•  $7x+2+18=6x+3+20$ 

Multiple Choice

If x = 13, how would you find TQ?

•  $2\left(13\right)-5$ 

•  $2\left(13\right)-5+18$ 
  

•  $2\left(13\right)+1$ 

•  $2\left(13\right)+1+14$ 

Multiple Choice

If x = 13, how would you find RS?

•  $2\left(13\right)-5$ 

•  $2\left(13\right)-5+18$ 
  

•  $2\left(13\right)+1$ 

•  $2\left(13\right)+1+14$ 

When they intersect OUTSIDE the circle

• a is the outside, (a+b) is the whole

• c is the outside, (c+d) is the whole

• outside(whole) = outside(whole)

Multiple Choice

Which formula would you use to find a segment length in this image?

• $ab=cd$

• $a+b=c+d$

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

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

Multiple Choice

Which equation would you use to solve for x?

•  $9+x=8+19$  

•  $9x=8\cdot19$  

•  $9\cdot8=19x$  

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

Multiple Choice

Which equation would you use to solve for x?

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

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

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

•  $8+3x+4=7+5x+2$  

What if a is the outside and the whole?

Multiple Choice

Which equation would you use to solve for x?

• $18x=24$

• $18x^2=24$

• $24^2=18x$

• $24^2=18\left(18+x\right)$

Multiple Choice

Which equation would you use to solve for x?

•  $x^2=27\cdot21$ 

•  $x^2=27\left(27+21\right)$ 

•  $27^2=21x$ 

•  $27^2=21\left(21+x\right)$ 

Multiple Choice

Which equation would you use to solve for x?

• $$3x^2=9\left(9+16\right)$$

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

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

• $$3x^2=9\left(16\right)^{ }$$