Thread: Cabins B and G

Cabins B and G are located on the shore of a circular lake, and cabin L is located near the lake. Point D is a dockon the lake shore and is collinear with cabins B and L. The road between cabins G and L is 8 miles long and is tangent to the lake. The path between cabin L and dock D is 4 miles long.

Hello, magentarita!

Your forgot to give us the question . . .

Cabins and are located on the shore of a circular lake,
and cabin is located near the lake.
Point is a dock on the lake shore, collinear with cabins and .
The road between cabins and is 8 miles long and is tangent to the lake.
The path between cabin and dock is 4 miles long.

Code:

         B    * * *
          o           *
        *   \           *
       *      \          *
                \  x
      *           \       *
      *             \     *
      *               \   *
                        \  D
       *                 o
        *               *   \  4
          *           *       \
              * o * - - - - - - o L
                G         8

The only questions we can answer are:
. . What are the distances amd ?


If that is indeed the question, we should know this theorem:

. . If a tangent and a secant are drawn to a circle from an external point,
. . the tangent is the mean proportional between the external segment
. . of the secant and the entire secant.


In this problem, we have: .

Then: .


Therefore: . miles.

Originally Posted by Soroban

Hello, magentarita!

Your forgot to give us the question . . .

Code:

         B    * * *
          o           *
        *   \           *
       *      \          *
                \  x
      *           \       *
      *             \     *
      *               \   *
                        \  D
       *                 o
        *               *   \  4
          *           *       \
              * o * - - - - - - o L
                G         8

The only questions we can answer are:
. . What are the distances amd ?


If that is indeed the question, we should know this theorem:

. . If a tangent and a secant are drawn to a circle from an external point,
. . the tangent is the mean proportional between the external segment
. . of the secant and the entire secant.


In this problem, we have: .

Then: .


Therefore: . miles.

Tell me, how do you make such beautiful geometric shapes with your keyboard?