points h and f lie on circle c. what is the length of line segment gh? 3 units 4 units 5 units 6 units

Answer:

3 units

Explanation:

Step1: Identify right - triangle

In right - triangle EGC, EC = 9 (radius) and EG = 12.

Step2: Use Pythagorean theorem

By the Pythagorean theorem (GC=\sqrt{EG^{2}+EC^{2}}=\sqrt{12^{2}+9^{2}}=\sqrt{144 + 81}=\sqrt{225}=15).

Step3: Let (GH=x) and (HC = 9) (radius)

We know that (GC=GH + HC).

Step4: Solve for (GH)

Since (GC = 15) and (HC=9), then (GH=GC - HC=15 - 12=3) units.