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Byju's Answer
Standard IX
Mathematics
Postulate5
6. Let ABC be...
Question
6. Let ABC be a right-angled triangle with /_B=90 degree. Let I be the incentre of ABC. Let AI extended intersect BC at F. Draw a line perpendicular to AI at I. Let it intersect AC at E. Prove that IE=IF.
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Similar questions
Q.
Let
A
B
C
be a triangle in which
A
B
=
A
C
and let
I
be its in-centre. Suppose
B
C
=
A
B
+
A
I
. Find
∠
B
A
C
.
Q.
In a triangle
A
B
C
,
let
H
denote its orthocentre. Let
P
be the reflection of
A
with respect to
B
C
.
The circumcircle of
△
A
B
P
intersects the line
B
H
again at
Q
,
and the circumcircle of
△
A
C
P
intersects the line
C
H
again at
R
.
Prove that
H
is the incentre of
△
P
Q
R
.
Q.
Let
A
B
C
be an isosceles triangle with
A
B
=
A
C
. Let be its circumcircle and let
O
be the centre of Let
C
O
meet in
D
. Draw a line parallel to
A
C
through
D
. Let it intersect
A
B
at
E
. Suppose
A
E
:
E
B
=
2
:
1
then
A
B
C
is an equilateral triangle.
Q.
Let
A
B
C
be a right-angled triangle with
∠
B
=
90.
Let
B
D
be the altitude from
B
on to
A
C
.
Let
P
,
Q
and
I
be the incentres of triangles
A
B
D
,
C
B
D
,
and
A
B
C
,
respectively. Show that the circumcentre of the triangle
P
I
Q
lies on the hypotenuse
A
C
.
Q.
Here
△
ABC is a right angle triangle with right angle at C. Let BC =a , Ca = b, AB = c. Let P be the length of the perpendicular from C on AB. Prove that (i) Pc = ab.
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