G.11 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?

• $$2\left(13\right)-5$$

• $$2\left(13\right)-5+18$$

• $$2\left(13\right)+1$$

• $$2\left(13\right)+1+14$$

Multiple Choice

Solve for x

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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?

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

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

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

• $$8+3x+4=7+5x+2$$  

Multiple Choice

Solve for x

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• 8.7

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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?

• $$3x^2=9\left(9+16\right)$$

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

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

• $$3x^2=9\left(16\right)^{ }$$

Multiple Choice

Solve for x

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Multiple Choice

Solve for x

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• 1.7

• 2.1

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Multiple Choice

Solve for x

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• 25.33

• 18.76

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Multiple Choice

Solve for x

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• 1.5

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Multiple Choice

Solve for x

• 6.3

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• 4.9

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Exterior Angle

Fill in the Blanks

Multiple Choice

Solve for x.

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Interior Angle

• An interior angle has a vertex inside the circle and is formed by two intersecting chords/secants.

• The measure of an interior angle is half the sum of its corresponding arcs.

• (arc1 + arc2)/2

Multiple Choice

What is the measure of the angle DBC?

• $$m\angle DBC=65\degree$$

• $$m\angle DBC=87.5\degree$$

• $$m\angle DBC=120\degree$$

• $$m\angle DBC=62.5\degree$$

Fill in the Blanks

Multiple Choice

Find the measure of  $$\angle KML$$ .

• $$m\angle KML=10\degree$$  

• $$m\angle KML=75\degree$$  

• $$m\angle KML=42.5\degree$$  

• $$m\angle KML=47.5\degree$$  

Fill in the Blanks

Fill in the Blanks

With tangents and secants, there is an intersection point OUTSIDE the circle. Formula is half the difference of the arcs.

The question asks us to find the outside angle C. How can we do that if we're only given one angle?

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

Multiple Choice

It's the final slide! What is the value of x?

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