Math Is Fun Forum

Enshrouded_

Member

Registered: 2015-07-31

Posts: 47

2 Geometry Problems

In rectangle

, we have

and

. Let

be the midpoint of

, and let

be the point such that

,

, and

and

lie on opposite sides of

. Find

, in degrees.

Let

,

,

,

be twelve equally spaced points on a circle with radius 1. Find

(The sum includes the square of the distance between any pair of points, so the sum includes

terms.)

Last edited by Enshrouded_ (2015-09-12 15:23:41)

Bob

Administrator

Registered: 2010-06-20

Posts: 10,626

Re: 2 Geometry Problems

hi Enshrouded_

As DM = XM and also CM by symmetry, a circle centred on M will go through D, X and C.

With DX as a chord and C as a point on the circumference, angle DMX = 2 times DCX.
(angle properties of a circle: http://www.mathisfunforum.com/viewtopic.php?id=17799 post 6.)

You will find a hint for the second one here:

http://www.mathisfunforum.com/viewtopic.php?id=22500

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob