Consider an equilateral triangle 4ABC with unit side length. Let M be the midpoint of side
AB. A ball is released in a straight line from M and bounces o the side BC at a point D.
Then, it bounces o the side CA at a point E and lands exactly at B. By the law of re
ection,
we have \BDM = \CDE and \CED = \AEB. Calculate MD + DE + EB, the distance
that the ball travels before reaching B. Choose the correct choice from the following answers:
A) √12/2
B) √11/2
C) √13/2
D) √14/2
E) √17/2
The solution can be obtained by re   ecting the triangle across edge CB to obtain   another equilateral triangle 4A0CB, and then across A0C to get 4A0B0C. The length of the   line MB0 is the minimum distance from M to the vertex B that hits both sides BC and CA0.   The length of the line segment BB0 is   √3/2   Thus, the length of MB =√1+3/4=√13/2   correct answer √13/2
<result>C</result>
Consider an equilateral triangle 4ABC with unit side length. Let M be the midpoint of side
AB. A ball is released in a straight line from M and bounces o the side BC at a point D.
Then, it bounces o the side CA at a point E and lands exactly at B. By the law of re
ection,
we have \BDM = \CDE and \CED = \AEB. Calculate MD + DE + EB, the distance
that the ball travels before reaching B.