Math Is Fun Forum

MathWA

Member

From: Somewhere over the rainbow

Registered: 2016-05-22

Posts: 12

Website

Circles with MD

In the circle, minor arc RS=409, then mdW+mdT equals what?
Here's the image:

I don't understand what md means.
Please explain your work. Thank you!

The picture is on my AOPS forum:

[I added the url and the image - bobbym]

http://artofproblemsolving.com/communit … es_with_md

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We cannot solve our problems with the same thinking we used when we created them.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circles with MD

hi MathWA

Welcome to the forum.

I followed this back to the AoPS page and got a 'lack of the right font' error message.

I agree with ishankhare's interpretation since it actually leads to a problem that can be done.

Some mathematicians use a little m to mean 'the measure of'.  It can be used for either a length or an angle measure so I avoid it myself as I think it creates confusion.

Firstly you're told the (angle) measure of the arc RS.  If C is the centre of the circle this means that angle RCS is 40 degrees.

There is a Euclidean theorem that the angle at the centre is twice the angle at the edge of the circumference (see http://www.mathisfunforum.com/viewtopic.php?id=17799 posts 6 and 7)

So angle RWS = 20 = angle RTS. 

So the problem makes sense if it's asking what these two angles add up to.

Hope that helps,

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

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Circles with MD

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circles with MD

Oh.  To describe an angle you really need the three points that make the angle eg. MWS.  I was assuming the question meant RWS.

If it's MWS + RWM then that won't be 180 as the points aren't cyclic.

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

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Circles with MD

Last edited by thickhead (2016-05-22 23:06:48)

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Circles with MD

Thanks for clearing that up .

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

thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: Circles with MD

My suggestion was intended for MathWa to do the rest.

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{1}Vasudhaiva Kutumakam.{The whole Universe is a family.}
(2)Yatra naaryasthu poojyanthe Ramanthe tatra Devataha
{Gods rejoice at those places where ladies are respected.}