Answer:
EF = 12.4
Step-by-step explanation:
To find the length of the tangent segment EF, we can use the Intersecting Secant-Tangent Theorem.
The Intersecting Secant-Tangent Theorem states that when a tangent and a secant intersect at a point outside a circle, the square of the length of the tangent segment is equal to the product of the lengths of the secant segment and its external segment.
In this case:
- Tangent segment = EF
- Secant segment = HF = 8 + 9 = 17
- External secant segment = GF = 9
Therefore:
[tex]EF^2=17\cdot9\\\\EF^2=153\\\\EF=\sqrt{153}\\\\EF=12.3693168768...\\\\EF=12.4\; \sf (nearest\;tenth)[/tex]
So, the length of EF is 12.4, rounded to the nearest tenth.
