Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Let be the orthocentre of triangle
MATHEMATICS · Subjective · CBSE · Mathematics · Triangles · Triangles
Problem
Let
H
H
H
be the orthocentre of triangle
A
B
C
ABC
A
B
C
. Let
M
M
M
be the midpoint of
B
C
BC
B
C
. Let the ray
H
M
HM
H
M
be extended beyond
M
M
M
to meet the circumcircle
(
A
B
C
)
(ABC)
(
A
B
C
)
again at
P
P
P
. Prove that
H
C
P
B
HCPB
H
C
P
B
is a parallelogram.
Related theory
Quadrilaterals
Distance and Section in the Plane
Similarity
Triangle similarity conditions
Similarity of triangles
Triangles
Browse the problem library