Grassland and goat

An unfenced grassland is a right triangle ABC with AB = 4m, BC = 8m, and AC as hypotenuse. A goat is tied to a 5-m long rope with its stake at point O, which is 2m from side AB and 2m from the prolongation of side BC through corner B. Then:

1. How far is O from C in meters?
2. Determine the area in which the goat can graze inside the land ABC.
3. If the land was fenced on sides AB and BC, determine where the goat can graze inside the land ABC.

Correct answer:

c₁ =  0 m

Step-by-step explanation:

$$\begin{gathered} AB=4\text{m} \\ BC=8\text{m} \\ r=5\text{m} \\ {a}_1=2\text{m} \\ {b}_1=2\text{m} \\ AC=\sqrt{A{B}^2+B{C}^2}=\sqrt{4^2+8^2}=4\sqrt{5}\text{m}\doteq 8.9443\text{m} \\ {c}_1=0=0\text{m} \end{gathered}$$

Try another example