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If is the orthocentre of an acute triangle
MATHEMATICS · Multi correct · CBSE · Mathematics · Triangles · Triangles
Problem
If
H
H
H
is the orthocentre of an acute triangle
A
B
C
ABC
A
B
C
,
R
R
R
is its circumradius,
r
r
r
its inradius, and
P
=
A
H
+
B
H
+
C
H
P=AH+BH+CH
P
=
A
H
+
B
H
+
C
H
, then: (1)
P
=
2
(
R
+
r
)
P=2(R+r)
P
=
2
(
R
+
r
)
(2) The maximum value of
P
P
P
is
3
R
3R
3
R
. (3) The minimum value of
P
P
P
is
3
R
3R
3
R
. (4)
P
=
2
(
R
−
r
)
P=2(R-r)
P
=
2
(
R
−
r
)
Related theory
Properties of Triangles
Triangle Properties
Similarity
Triangles
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