Question

Question 3 of 3Federico enjoys catching pokemons in university campus. One day, while trying to catch charmander, hefound the best spot next to a perfectly circular pond. He was 50 feet from the bank and 71 feet from thepoint of tangency. Determine the radius of the pond using the given information. Round to the nearestinteger

Answer 1

To solve this problem, we will use the following diagram as reference,

Now, from the Pythagorean theorem, we know that ( we will omit the units to simplify the calculations):

$(r+50)^2=71^2+r^2.$

Simplifying the above equation, we get:

$\begin{gathered} r^2+100r+2500=71^2+r^2, \\ 100r+2500=5041. \end{gathered}$

Solving the above equation for r, we get:

$\begin{gathered} 100r=5041-2500, \\ r=\frac{5041-2500}{100}=25.41. \end{gathered}$

Answer:

$25\text{ ft.}$