Answer:
4 1/2
Explanation:
If two chords intersect in a circle, the product of the lengths of the segments of one chord equal the product of the segments of the other.
JH * HK = GH * HI
3 * (2x+1) = 2 ( x+5)
Distribute
6x+3 = 2x+10
Subtract 2x from each side.
6x-2x+3 = 2x-2x+10
4x+3 = 10
Subtract 3 from each side.
4x = 10-3
4x= 7
Divide by 4.
x = 7/4
Now find HK.
HK = 2x+1
= 2(7/4)+1
= 7/2+1
= 9/2
= 4 1/2