Difference between revisions of "1960 IMO Problems/Problem 4"
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==See Also== | ==See Also== | ||
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Revision as of 19:04, 15 September 2012
Problem
Construct triangle , given
,
(the altitudes from
and
), and
, the median from vertex
.
Solution
Let ,
, and
be the midpoints of sides
,
, and
, respectively. Let
,
, and
be the feet of the altitudes from
,
, and
to their opposite sides, respectively. Since
, with
, the distance from
to side
is
.
Construct with length
. Draw a circle centered at
with radius
. Construct the tangent
to this circle through
.
lies on
.
Draw a circle centered at with radius
. Construct the tangent
to this circle through
.
lies on
. Then
.
Construct the line parallel to
so that the distance between
and
is
and
lies between these lines.
lies on
. Then
.
See Also
1960 IMO (Problems) | ||
Preceded by Problem 3 |
1 • 2 • 3 • 4 • 5 • 6 • 7 | Followed by Problem 5 |