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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 160

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

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

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

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,526

An alternative way to work it out is:

XAY

YAB

XAB

XBA

ZAC (=ZCA)

Here lies the reader who will never open this book. He is forever dead.

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

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**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 160

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

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,395

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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