Question

Find the value of the variable and the length of each chord.

y=
DE =
FG =

Answer 1

y=6

DE=7

HG=8

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:

`DH* HE=FH* HG\\\\3* 4=2y\\\\12=2y\\\\y=6`

Hence, the length of the segment HG is 6

The length of a chord is equivalent to the sum of its segments;

`DE=DH+HE\\\\=3+4\\\\=7\\\\\\FG=FH+HG\\\\=2+6\\\\=8`