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Byju's Answer
Standard XII
Mathematics
Trigonometry
A triangle ha...
Question
A triangle has sides 6,7,and 8. The line through its incenter parallel to the shortest side is drawn to meet the other two sides at P and Q Then find the 7 times of length of the segment PQ ?
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Solution
Δ
=
r
×
s
∴
21
×
r
2
=
1
2
b
×
h
=
6
×
h
2
=
3
h
or
r
h
=
2
7
Now
A
P
Q
and
A
B
C
are similar.
Thus,
h
−
r
h
=
P
Q
6
⇒
1
−
r
h
=
P
Q
6
⇒
1
−
2
7
=
P
Q
6
⇒
5
7
=
P
Q
6
⇒
P
Q
=
30
7
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