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Answer:
OC=X
in triangle AOB,
AB²=OB²+AO²
8²=(6+X)²+AO²
64=36+x²+12x+AO²
AO²=64-36-x²-12x=28-x²-12x...... equation 1
in triangle AOC,
AC²=OC²+AO²
3²=x²+AO²
9=x²+AO²
AO²=9-x²....... equation 2
equation 1=equation 2=AO²
28-x²-12x=9-x²
28-12x=9
28-9=12x
19=12x
x=19/12==1.58cm
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