Devinegracepaceloidn
Answered

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B. Find the length of the unknown segment (x) in each of the following figures.​

B Find The Length Of The Unknown Segment X In Each Of The Following Figures class=

Sagot :

KAntoineDoixidn

✒️POWER THEOREMS

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[tex] \large\underline{\mathbb{ANSWERS}:} [/tex]

[tex] \qquad \Large \:\: \rm{1) \; x = 10.5 \: units} [/tex]

[tex] \qquad \Large \:\: \rm{2) \; x = 4 \: units} [/tex]

[tex] \qquad \Large \:\: \rm{3) \; x = 9 \: units} [/tex]

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[tex] \large\underline{\mathbb{SOLUTIONS}:} [/tex]

#1: By according to the Chord-Chord Power Theorem, the given suggests that:

  • [tex] (ON)(NA) = (RN)(NM) [/tex]

» Substitute the given and then find x.

  • [tex] (8)(x) = (12)(7) [/tex]

  • [tex] 8x = 84 [/tex]

  • [tex] \frac{\,8x\,}{8} = \frac{\,84\,}{8} \\ [/tex]

  • [tex] x = 10.5 [/tex]

[tex] \therefore [/tex] The length of segment x is 10.5 units

[tex] \: [/tex]

#2: By according to the Tangent-Secant Power Theorem, the given suggests that:

  • [tex] (VE)^2 = (VL)(VO) [/tex]

» Substitute the given and then find x.

  • [tex] (10)^2 = (25)(x) [/tex]

  • [tex] 100 = 25x [/tex]

  • [tex] \frac{\,100\,}{25} = \frac{\,25x\,}{25} \\ [/tex]

  • [tex] 4 = x [/tex]

[tex] \therefore [/tex] The length of segment x is 4 units

[tex] \: [/tex]

#3: By according to the Secant-Secant Power Theorem, the given suggests that:

  • [tex] (IS)(IH) = (IT)(IF) [/tex]

  • [tex] (IS)(IH) = (IF + FT)(IF) [/tex]

» Substitute the given and then find x.

  • [tex] (16)(x) = (8 + 10)(8) [/tex]

  • [tex] (16)(x) = (18)(8) [/tex]

  • [tex] 16x = 144 [/tex]

  • [tex] \frac{\,16x\,}{16} = \frac{\,144\,}{16} \\ [/tex]

  • [tex] x = 9 [/tex]

[tex] \therefore [/tex] The length of segment x is 9 units

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