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WOLFRAM|DEMONSTRATIONS PROJECT

Three Equal Segments from the Altitudes of a Triangle

labels
altitudes
circles
segments
In the triangle
P
1
P
2
P
3
let the feet of the altitudes be
Q
1
,
Q
2
, and
Q
3
. The circle with diameter
P
1
Q
1
meets
P
1
P
2
and
P
1
P
3
at two points other than
P
1
to form a segment of length
l
1
; similarly define
l
2
and
l
3
. Prove that
l
1
=
l
2
=
l
3
.
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