Find the measure of angle dca if d is the incenter of the triangle abc.

First we have to understand what incenter is.

Incenter of a triangle is the point where the angle bisectors intersects.

It means

And sum of measurement of angles of a triangle = 180

Therefore,

geometry: triangles

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call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584

the answer is two. hope this !