Prove squareness - geometry

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Yellybean

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Jul 6, 2014
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Hello,
I would like to ask for a hint for this example.
Let ABC be a triangle, where where BC is the shortest side. Mark the middle of BC as M. On the side AB we mark point X, and on the side AC we mark point Y, so that it applies |BX| = |BC| = |CY|. Intersection of lines CX and BY mark Z. Prove that the line ZM passes through the center of the circle ascribed to side BC.


Thank you very much for any hint.

Yelly
 
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There are 3 basic types of circles in triangle:
circle inscribed = the intersection of the axes of angles
circle circumscribing = the intersection of the axes of sides
circle attributed (ascribed) or i dont know exact word, but there are 3. Middle of this circle is in the intersection of axes of exterior angle
this:Excircles_and_Nagel_point.JPG
 
Yellybean said:
Hello,
I would like to ask for a hint for this example.
Let ABC be a triangle, where where BC is the shortest side. Mark the middle of BC as M. On the side AB we mark point X, and on the side AC we mark point Y, so that it applies |BX| = |BC| = |CY|. Intersection of lines CX and BY mark K. Prově that line ZM. Prove that the line KZ passes through the center of the circle ascribed to side BC.


Thank you very much for any hint.

Yelly
Click to expand...

What does that mean?
 
Yellybean said:
Hello,
I would like to ask for a hint for this example.
Let ABC be a triangle, where where BC is the shortest side. Mark the middle of BC as M. On the side AB we mark point X, and on the side AC we mark point Y, so that it applies |BX| = |BC| = |CY|. Intersection of lines CX and BY mark K. Prove that the line KZ passes through the center of the circle ascribed to side BC.


Thank you very much for any hint.

Yelly
Click to expand...

Where is point Z?
 
Let ABC be a triangle, where where BC is the shortest side. Mark the middle of BC as M. On the side AB we mark point X, and on the side AC we mark point Y, so that it applies |BX| = |BC| = |CY|. Intersection of lines CX and BY mark Z. Prove that the line ZM passes through the center of the circle ascribed to side BC.

It's the intersection of lines CX and BY
 
triangle.jpg
Okay, here is the picture.

Triangle ABC, BC is the shortest side.
M = middle of side BC
X the point on the side AB >>> |BX| = |BC|
Y the point on the side AC >>> |CY| = |BC|
Z = intersection of lines CX and BY

Prove, that the line MZ (green line) crosses the middle of excircle to the side BC.
 
yes. I was trying to show that ZBSC is a rectangle. I tried to express BCS as the angle (180 - gama) / 2 and show that it must be same as angle ZBC. But im still not done with that.
 
Well, i did what you wrote and i must ask you, did you understand a question? Why would i prove that AS and XS intersects in point S? Of course they do, any two lines intersect in 1 point (if they aren't parallel, or same).
I need to show why ZM intersect S.
 
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I have already solved it by another way (much easier than you recommend). But thank you. It wasnt hard. Goodbye
 
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