Sunday

November 23, 2014

November 23, 2014

Posted by **Anonymous** on Monday, August 19, 2013 at 11:56am.

- geometry -
**Steve**, Monday, August 19, 2013 at 1:59pmGeometrically, I have no idea. Algebraically, if we let

A = (0,0)

B = (1,0)

then

D = (1,√3)

X = (1,-1)

so

M = (1,(√3-1)/2)

C = (3/2,√3/2)

slope of MC is 1

slope of MD is √3/2

∠CMD = 60°-45° = 15°

Maybe by working with all those 60° and 30° angles in the figure this will become clear geometrically.

- geometry -
**exactly**, Wednesday, October 2, 2013 at 4:48amWell, I sort of get a different answer: ∠CMD = 45

Here's how I got it:

Let CD = x. It is trivial by law of cosine that: BD = x√3

Whence DM = (√3 + 1)/2 * x. Let us denote the midpoint of BD as K. Then it is easy to see that:

MK = DM - DK = x/2. Now it is trivial to end of to get:

<CMD = tan^(-1) 1 = 45.

Well, since the live period is long over I suppose we can discuss. In the future, please refrain from posting live brilliant questions :)

**Answer this Question**

**Related Questions**

geometry - The area of a particular regular hexagon is x^3 square units, where x...

Geometry - ABCDEF is a regular hexagon with side length 43√4. Points G,H,I...

Math - ABCDEF is a regular hexagon with side length 4 (Under 4 root)√3. ...

Math - ABCDEF is a regular hexagon with side length 4 (Under 4 root)√3. ...

help hexagon geometry - A regular hexagon is inscribed in a circle and another ...

geometry - Hexagon A is a regular hexagon. The total length of all the sides of ...

geometry - Hexagon D and hexagon H are regular hexagons. The scale factor from ...

math - ABCDEF is a regular hexagon. If the perimeter = 12 find the area of ...

GEOMETRY - In a figure ABCDEF is a regular hexagon with DH=1cm and HC=2cm. Find...

math - how do you find the area of a hexagon? Here is the formula: Area of ...