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Incircle tangents in a triangle

  • Thread starter soopo
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  • #1
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Homework Statement


In triangle ABC, there is a maximun circle (3 intersection points) such that the lengths of the triangles are 3 : 4 : 5. A ray from the smallest angle C is tangential to the opposite side. Another ray from the greatest angle B is also tangential to the opposite side.

Find p : q where p is the length between the ray from the greatest angle to the tangential point and the intersection of this ray to another ray from smaller angle;
q is the length between the intersection of two rays and the vertex C.


The Attempt at a Solution



The problem can be solved by Mass point geometry and areas/lengths.
However, I am not sure about the ratios of how the rays divide triangle's two sides.

We do know that whether the rays are bisectors although they meet inside the circle.

How would you solve the problem?
 

Answers and Replies

  • #2
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I don't follow your description of the problem. Is there a picture you can upload? I don't know where the extra triangles are, unless that was a typo in the first line.
 
  • #3
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I don't follow your description of the problem. Is there a picture you can upload? I don't know where the extra triangles are, unless that was a typo in the first line.
The problem in the original form:

A circle inscribed in a 3-4-5 triangle. A segment is drawn from the smaller acute angle to the point of tangency on the opposite side. This segment is divided in the ratio p : q by the segment drawn from the larger acute angle to the point of tangency on its opposite side. If p > q then find p : q.

The same problem is in the following picture at
http://dl.getdropbox.com/u/175564/problem2.JPG [Broken]
You can see a triangle which shows you how I understand the question.
 
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