Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ π -¹ ² ³ °

You are not logged in.

- Topics: Active | Unanswered

Pages: **1**

**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 178

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,916

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

Offline

**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,919

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

The knowledge of some things as a function of age is a delta function.

Offline

**cooljackiec****Member**- Registered: 2012-12-13
- Posts: 178

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

Offline

**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,916

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

Offline

Pages: **1**