Expert: Bobby Soltani - 11/24/2005

Question
Can you explain how to come up with the follwing:

1. What is the maximum number of distinct diagonals that can be drawn in a hexagon?
(answer:9)

2. In the standard (x,y) coordinate plane, the center of the circle lies on the x-axis at x=4. If the circle is tangent to the y-axis, which of the following is an equation of the circle?
(anser: (x-4)squared + ysquared =16

Answer
Hi Amanda,

1.  First, draw a hexagon.  Then, from a single point draw all diagonals from that point.  You will find that there are three diagonals.  Now, since there are six points, and three diagonals per point, we know that there are 18 total diagonals.  But, this counts each diagonal twice, so we have to divide the 18 by 2 to get 9 unique diagonals.

2.  The equation for a circle is

(x - h)^2 + (y - k)^2 = r^2

where (h,k) is the coordinates of the center of the circle and r is the radius.

In the standard (x,y) coordinate plane, the center of the circle lies on the x-axis at x=4.  That means that the center is at (4,0), so h = 4, and y = 0.  If the circle is tangent to the y-axis, which of the following is an equation of the circle?  If the circle touches the y axis which is x = 0 and the center is at x = 4, then the radius is equal to 4.  Drawing the circle may help you if you are confused.

Now, plug in h,k, and r into the equation.

(x - 4)^2 + (y - 0)^2 = 4^2

(x - 4)^2 + y^2 = 16

Let me know if you have any questions.

Bobby