Math Is Fun Forum

denis_gylaev

Member

Registered: 2015-03-19

Posts: 66

Geometry

I am stuck on these two problems, a solution would be greatly appreciated

Triangle ABC is a right triangle with right angle at A. Suppose

is an altitude of the triangle, 

is an angle bisector of the triangle, and

is a median of the triangle, and

. If X is on

, then what is the measure of

Points D, E, and F are the midpoints of sides

respectively, and

is an altitude of the triangle. If

, then what is

in degrees?

Many Thanks

Last edited by denis_gylaev (2015-08-06 09:35:27)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometry

Hi;

For the first one I am getting 32 degrees, what are you getting?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,621

Re: Geometry

hi denis_gylaev

Q1. A circle, centred on Z will go through A, B and C (because it's the midpoint of BC and because there's a 90 angle at A)

So AZ = CZ

You can get ACB by angle sum of triangle and straight line and hence ZAC.

Q2. Someone else asked this recently.  The nine point circle of ABC goes through D, E, F and Z so EZD = EFD.

DEF is similar to ABC.

It's a while since I proved the properties of the nine point circle, so if you want that too, I'll have to do some research first.

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