1954 AHSME Problems/Problem 19
Problem 19
If the three points of contact of a circle inscribed in a triangle are joined, the angles of the resulting triangle:
Solution
For the sake of clarity, let the outermost triangle be with incircle tangency points
,
, and
on
,
and
respectively. Let
, and
. Because
and
are isosceles,
and
. So
, and since
,
is acute.
The same method applies to and
, which means
is acute - hence our answer is
.