Let ABC be an equilateral triangle with side length 2.
Let the altitude AA' and a cevian BB' intersect at a point D.

If the incircles of triangles ABB' and BCD are congruent, then what is the value of their common radius?

Cevian.  A term I didn't know and still know little about after some 48 hours or so. 

I devised my drawing; always a good way to start. 

My equilateral has two cevian lines emanating from B and C respectively and intersecting on the opposite side at B' and C' having both passed through point D which lies on the cevian line AA' which is both the altitude and bisector of the triangle.

D is situated slightly above the median of the equilateral.  The cevians are both cotangent to the two incircles.

There are some interesting similar triangles with respect to vertex A and also from the cevian base of B and C.  Unfortunately at their points of exit, BB' and CC' do not form a right angle.

At this point I am lost.  Do I need to employ something like sine/cos rule, or will ratios and angular comparisons get me there?

Posted by brianjn on 2008-04-18 09:58:51