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#1 2013-04-29 11:08:32

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

triangles!!!

Triangle ABC is a right triangle with right angle at A. Suppose AX is an altitude of the triangle, AY is an angle bisector of the triangle, and  AZ is a median of the triangle, and angle XAY=13. If X  is on BY, then what is the measure of angle ZAC?


I see you have graph paper.
You must be plotting something
lol

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#2 2013-04-29 19:38:53

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,539

Re: triangles!!!

hi cooljackiec

I assumed that Y and Z are on the line BC.

Because Z is the midpoint of BC and there is a right angle at A, Z is the circumcentre of ABC.  ie.  A circle centred on Z will go through A, B and C.

So ZA = ZC and ZAC is isosceles.

So work oiut angles in this order:

XAY
XYA
YAC
ZCA (= YCA)
ZAC

Bob

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You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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#3 2013-04-29 22:55:04

anonimnystefy
Real Member
From: The Foundation
Registered: 2011-05-23
Posts: 15,673

Re: triangles!!!

An alternative way to work it out is:
XAY
YAB
XAB
XBA
ZAC (=ZCA)


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“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment

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#4 2013-04-30 10:54:02

cooljackiec
Member
Registered: 2012-12-13
Posts: 162

Re: triangles!!!

oh yea, isoceles triangles! median of hypotenuse = half of hyptenuse. i get it

I got 32. not sure, this seems incorrect

Last edited by cooljackiec (2013-04-30 11:24:27)


I see you have graph paper.
You must be plotting something
lol

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#5 2013-04-30 19:02:13

bob bundy
Moderator
Registered: 2010-06-20
Posts: 6,539

Re: triangles!!!

That's good.  32 is my answer too.

Bob


You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei

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