+ 7 4 5x 1 x 6 10 + 1 2mathbygrosvenor.weebly.com/uploads/1/3/4/8/13488403/geo... · 2018. 9....
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Name: _________________________________________________ Segment Relationships on Circles Now that you know what the parts that interact with a circle are called, it’s time to learn how to evaluate them (determine their value). All of the parts on a circle have a specific relationship. For example, a diameter is always twice as big as a radius. If you know the rules of those relationships, then you can use those rules to solve problems. Today, we’re going to focus on the segments. Here are the three rules that govern tangents, secants, and chords… TangentTangent Touching Tangents are equal. SecantTangent or SecantSecant If you multiply the outside part of one segment with the whole thing, it will equal the outside of the other multiplied by the whole thing. ChordChord If you multiply the two parts of one chord, it will equal the product of the two parts of the chord that crosses it. = EX: They’re equal, so… ! = ! 2 + 7 = 3 + 1 7 = + 1 6 = = 6 = ( )( ) EX: Secant: outside = 4, whole = 4 + x Tangent: outside = 6, whole = 6 ! ℎ ! = ( ! )(ℎ ! ) 4 4 + = 6 6 16 + 4 = 36 4 = 20 = 5 = Ex: Chord A: part1 =5x, part2 =2 Chord B: part1 = 10, part2 =1 !! !! = !! !! 5 2 = (10)(1) 10 = 10 = 1 Determine the value of x. EX There are two secants, so: Secantsecant Secant1: outside = 3, whole = 3 + 5 Secant2: outside = 2, whole = 2 + ! ℎ ! = ( ! )(ℎ ! ) 3 3 + 5 = 2 2 + 3 8 = 4 + 2 24 = 4 + 2 20 = 2 4 = = 4 1. 2. 3. 4. 5. 2x + 7 3x + 1 6 4 x 5x 2 1 10 2 x 3 5 4 2 x 3x 6 8 4 9x + 6 12x - 3 9x 2 6 15 8 x 6 10
Transcript of + 7 4 5x 1 x 6 10 + 1 2mathbygrosvenor.weebly.com/uploads/1/3/4/8/13488403/geo... · 2018. 9....
Name: _________________________________________________
Segment Relationships on Circles Now that you know what the parts that interact with a circle are called, it’s time to learn how to evaluate them (determine their value). All of the parts on a circle have a specific relationship. For example, a diameter is always twice as big as a radius. If you know the rules of those relationships, then you can use those rules to solve problems. Today, we’re going to focus on the segments. Here are the three rules that govern tangents, secants, and chords…
Tangent-‐Tangent Touching Tangents are equal.
Secant-‐Tangent or Secant-‐Secant If you multiply the outside part of one segment with the whole thing, it will
equal the outside of the other multiplied by the whole thing.
Chord-‐Chord If you multiply the two parts of one chord, it will equal the product of the two parts of the chord that crosses it.
𝒕𝒂𝒏𝒈𝒆𝒏𝒕𝟏 = 𝒕𝒂𝒏𝒈𝒆𝒏𝒕𝟐
EX:
They’re equal, so…
𝑡𝑎𝑛𝑔𝑒𝑛𝑡! = 𝑡𝑎𝑛𝑔𝑒𝑛𝑡! 2𝑥 + 7 = 3𝑥 + 1 7 = 𝑥 + 1
6 = 𝑥 𝑥 = 6
𝒐𝒖𝒕𝟏 𝒘𝒉𝒐𝒍𝒆𝟏 = (𝒐𝒖𝒕𝟐)(𝒘𝒉𝒐𝒍𝒆𝟐)
EX:
Secant: outside = 4, whole = 4 + x Tangent: outside = 6, whole = 6
𝑜𝑢𝑡! 𝑤ℎ𝑜𝑙𝑒! = (𝑜𝑢𝑡!)(𝑤ℎ𝑜𝑙𝑒!) 4 4 + 𝑥 = 6 6 16 + 4𝑥 = 36 4𝑥 = 20 𝑥 = 5
𝒑𝒂𝒓𝒕𝟏𝑨 𝒑𝒂𝒓𝒕𝟐𝑨 = 𝒑𝒂𝒓𝒕𝟏𝑩 𝒑𝒂𝒓𝒕𝟐𝑩 Ex:
Chord A: part1 = 5x, part2 = 2 Chord B: part1 = 10, part2 = 1 𝑝𝑎𝑟𝑡!! 𝑝𝑎𝑟𝑡!! = 𝑝𝑎𝑟𝑡!! 𝑝𝑎𝑟𝑡!!
5𝑥 2 = (10)(1) 10𝑥 = 10 𝑥 = 1
Determine the value of x. EX
There are two secants, so:
Secant-‐secant Secant1: outside = 3, whole = 3 + 5 Secant2: outside = 2, whole = 2 + 𝑜𝑢𝑡! 𝑤ℎ𝑜𝑙𝑒! = (𝑜𝑢𝑡!)(𝑤ℎ𝑜𝑙𝑒!)
3 3 + 5 = 2 2 + 𝑥 3 8 = 4 + 2𝑥 24 = 4 + 2𝑥
20 = 2𝑥 4 = 𝑥
𝑥 = 4
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2x + 7
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10
2 x
3 542x 3x6
84
9x + 6
12x - 3
9x
2
6
15 8x
610
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63
x5x + 12
7x - 4
5x
6910
2x + 6
4x + 2
8
10 x4 2x
6 10
7x
13
5
2x + 25
8x - 5 x15124
5
4
x
3x
68
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4
x
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6
510 x 6
x9
94x + 1
5x - 3
