Answer:
y=6
DE=7
HG=8
Step-by-step explanation:
-For chords intersecting each other within a circle, the product of their segments are always equal.
-We can therefore use this relationship to calculate the lengths of missing chords and segments as:
[tex]DH\times HE=FH\times HG\\\\3\times 4=2y\\\\12=2y\\\\y=6[/tex]
Hence, the length of the segment HG is 6
The length of a chord is equivalent to the sum of its segments;
[tex]DE=DH+HE\\\\=3+4\\\\=7\\\\\\FG=FH+HG\\\\=2+6\\\\=8[/tex]
