Park

Rotating sprayer irrigation lawns will permanently surround the newly built park. Find the largest radius of the circle that can be irrigated by sprayer P, not to spray park visitors online AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.

Correct answer:

r =  16.19 m

Step-by-step explanation:

$$\begin{gathered} a=55 \\ b=36 \\ c=28 \\ s=(a+b+c)/2=59.5 \\ r==? \\ T=\frac{ar}{2}=\sqrt{s(s-a)(s-b)(s-c)} \\ \frac{ar}{2}=\sqrt{s(s-a)(s-b)(s-c)} \\ r=\frac{2\sqrt{s(s-a)(s-b)(s-c)}}{a} \\ r=\frac{2\cdot \sqrt{59.5(59.5-55)(59.5-36)(59.5-28)}}{55} \\ r=16.19\text{m} \end{gathered}$$

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