Find Segment Lengths in Circles

Circles and Intersecting Lines

2 chords, 2 secants, 2 tangents, and 1 secant & 1 tangent

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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

Which equation would you use to solve for x?

• $$9x\ =\ 21\cdot27$$

• $$27x=9\cdot21$$

• $$21x=9\cdot27$$

• $$x+27\ =\ 9+21$$

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 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?

• $$3x^2=9\left(9+16\right)$$

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

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

• $$3x^2=9\left(16\right)^{ }$$

Tangent - Tangent Theorem

• Two intersecting tangents are equal to each other

• AB = CB

Multiple Choice

Find the length of BC.

• 2
• 3
• 9
• 14