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Byju's Answer
Standard X
Mathematics
SSS Similarity
Let ABC be an...
Question
Let ABC be an acute angled triangle. Let D and F be mid points of BC and AB respectively. Let perpendiculars from F to AC and perpendicular from B on BC meet at N . Prove that ND is the circumradius of AB
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Similar questions
Q.
Let
A
B
C
be a triangle such that
A
B
=
B
C
. Let
F
be the midpoint of
A
B
and
X
be a point on
B
C
such that
F
X
is perpendicular to
A
B
. If
B
X
=
3
X
C
then the ratio
B
C
A
C
equals
Q.
Let ABC be a triangle and let
B
B
1
,
C
C
1
be, respectively, the bisectors of
∠
B
,
∠
C
with
B
1
on AC and
C
1
on AB. Let
E
,
F
be the feet of perpendiculars drawn from
A
onto
B
B
1
,
C
C
1
,
respectively. Suppose
D
is the point at which the incircle of
Δ
A
B
C
touches
A
B
. Prove that
A
D
=
E
F
.
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.
Q.
A
B
C
is a right triangle right angled at
C
.
Let
B
C
=
a
,
C
A
=
b
,
A
B
=
c
and let
p
be the length of perpendicular from
C
on
A
B
prove that
i)
p
c
=
a
b
ii)
1
p
2
=
1
a
2
+
1
b
2
Q.
Let
A
B
C
be an acute-angled triangle triangle, and let
D
,
E
,
F
be points on
B
C
,
C
A
,
A
B
respectively such that
A
D
is the median,
B
E
is the internal angle bisector and
C
F
is the altitude. Suppose
∠
F
D
E
=
∠
C
,
∠
D
E
F
=
∠
A
a
n
d
∠
E
F
D
=
∠
B
. Prove that
A
B
C
is equilateral.
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