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  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

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Topic review (newest first)

bob bundy
2013-05-01 17:02:13

That's good.  32 is my answer too.

Bob

cooljackiec
2013-05-01 08:54:02

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

I got 32. not sure, this seems incorrect

anonimnystefy
2013-04-30 20:55:04

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

bob bundy
2013-04-30 17:38:53

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

cooljackiec
2013-04-30 09:08:32

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?

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