Answer:
The value of [tex]x[/tex] is 2.
Step-by-step explanation:
Given that [tex]\overline{HI}[/tex] and [tex]\overline{HJ}[/tex] are secant to arcs [tex]HI[/tex] and [tex]HJ[/tex], which have the same central angles. Therefore, [tex]HI = HJ[/tex] due to symmetry:
[tex]HI = HJ[/tex] (1)
[tex]2\cdot x + 1 = 5\cdot x - 5[/tex]
[tex]3\cdot x = 6[/tex]
[tex]x = 2[/tex]
Hence, the value of [tex]x[/tex] is 2.
