Answer:
HK = 13.6
Step-by-step explanation:
The given diagram shows a circle with two intersecting chords.
According to the Intersecting Chords Theorem, when two chords intersect inside a circle, the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord.
Therefore, in this case:
[tex]\sf HK \times KG = IK \times KJ[/tex]
Given that KG = 34, I = 21 and KJ = 22, then:
[tex]\sf HK \times 34 = 21 \times 22[/tex]
Solver for HK:
[tex]\sf HK=\dfrac{21 \times 22}{34}\\\\\\HK=\dfrac{462}{34}\\\\\\HK=13.5882352941...\\\\\\HK=13.6\; (nearest\;tenth)[/tex]
Therefore, the length of segment HK rounded to the nearest tenth is:
[tex]\Large\boxed{\boxed{\sf HK=13.6}}[/tex]
