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#1 2015-09-12 15:22:33

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.
1b39a7de7d5064e27d8ac7d0e00bb8b0db806199.png









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)

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#2 2015-09-12 19:49:09

Bob
Administrator
Registered: 2010-06-20
Posts: 10,053

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


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 smile

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