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Let x as the missing segment.
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According to the Thales theorem :
[tex] \frac{26}{x} = \frac{12}{36} \\ [/tex]
[tex] \frac{26}{x} = \frac{12}{12 \times 3} \\ [/tex]
[tex] \frac{26}{x} = \frac{1}{3} \\ [/tex]
Inverse both sides
[tex] \frac{x}{26} = \frac{3}{1} \\ [/tex]
[tex] \frac{x}{26} = 3 \\ [/tex]
Multiply sides by 26
[tex]26 \times \frac{x}{26} = 26 \times 3 \\ [/tex]
[tex]x = 26 \times 3[/tex]
[tex]x = 78[/tex]
Thus the missing segment has a measure of 78 .
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