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Triangle XYZ is inscribed in semicircle O shown below such that YZ = 7 and YX = 10. Which of the following
is closest to the radius of the semicircle?

(1) 5.8
(2) 6.1
(3) 11.6
(4) 12.2

Triangle XYZ is inscribed in semicircle O shown below such that YZ 7 and YX 10 Which of the following is closest to the radius of the semicircle 1 58 2 61 3 116 class=

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Answer:

(2)   6.1

tep-by-step explanation:

∠Y is a right angle, so ΔXYZ is a right triangle

[tex]XZ^{2} = XY^{2} + YZ^{2}[/tex]

[tex]XZ^{2} = 7^{2} + 10^{2}[/tex] = 49 + 100 = 149

XZ = [tex]\sqrt{149}[/tex] = 12.2

XZ is the diameter of the semicircle, therefore, the radius is 12.2/2 = 6.1

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