A women is taking a lesson in a circular swimming pool. she starts at one edge of the pool and swims for 12 meters in a straight line till hits the edge of the pool. she turns and swims another 5 meters and again hits the edge of the pool. she realizes that she is exactly on the opposite side of the pool where she started. what is the diameter of the pool ?

Question

A women is taking a lesson in a circular swimming pool. she starts at one edge of the pool and swims for 12 meters in a straight line till hits the edge of the pool. she turns and swims another 5 meters and again hits the edge of the pool. she realizes that she is exactly on the opposite side of the pool where she started. what is the diameter of the pool ?

I tried drawing a circle and plot the starting and the ending points and used the diameter formula but still did not work !!

thanks in advance..

Answer 1

I drew a triangle that 90 degree

and then applied this formula

square root (12^2+5^2)= 13

I don't know if it is right or not but still I can't prove it with the drawings.

Answer 2

you are correct. A right triangle inscribed in a circle has the diameter as its hypotenuse.

I don't know what you mean by "the diameter formula."

Answer 3

To find the diameter of the pool, we can use the Pythagorean theorem.

Let's visualize the situation.

1. Start by drawing a circle to represent the swimming pool.

2. Mark a point on the edge of the circle, representing the starting point.

3. Draw a straight line from the starting point to another point on the circle, representing the first 12-meter swim.

4. From this point, draw another line to the opposite side of the circle, representing the second 5-meter swim.

5. This point where the second swim ends should be exactly opposite to the starting point.

Now, we have formed a right-angled triangle inside the circle. The diameter of the circle will be the hypotenuse of this triangle.

To find the diameter, we can apply the Pythagorean theorem, which states that in a right-angled triangle:

a^2 + b^2 = c^2

Where:
a and b are the lengths of the two legs of the triangle, and
c is the length of the hypotenuse (the diameter in our case).

From the problem statement, we know that one leg of the triangle is 12 meters, and the other leg is 5 meters.

Let's substitute these values into the formula:

12^2 + 5^2 = c^2

144 + 25 = c^2

169 = c^2

Taking the square root of both sides:

c = sqrt(169)

c = 13

Therefore, the diameter of the pool is 13 meters.