2007 Indonesia MO Problems/Problem 1
Revision as of 15:04, 17 February 2020 by Rockmanex3 (talk | contribs) (Solution to Problem 1 — easy with a good diagram)
Problem
Let be a triangle with
. Let point
on side
such that
is the altitude, point
on side
such that
, and point
is the intersection of
and
. Prove that
.
Solution
By using the Angle Addition Postulate and substitution,
Since
is a 30-60-90 triangle,
.
Additionally, because is the foot of the altitude from
,
. Furthermore, by the Base Angle Converse, we must have
because
. Therefore, by AAS Similarity,
, so
. Thus,
.
Therefore, by substitution, .
See Also
2007 Indonesia MO (Problems) | ||
Preceded by First Problem |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 | Followed by Problem 2 |
All Indonesia MO Problems and Solutions |