if r+r1+r2-r3=4R cos×c
r1+r2+r3-r=4R
r+r1+r2=r3
then show c=90
Answers
Answer:
We know,
r
1
=4Rsin
2
A
cos
2
B
cos
2
C
r
2
=4Rsin
2
B
cos
2
C
cos
2
A
r
3
=4Rsin
2
C
cos
2
A
cos
2
B
r=4Rsin
2
A
sin
2
B
sin
2
C
Now,
r
1
+r
2
−r
3
+r=4R[4Rsin
2
A
cos
2
B
cos
2
C
+sin
2
B
cos
2
C
cos
2
A
−sin
2
C
cos
2
A
cos
2
B
+sin
2
A
sin
2
B
sin
2
C
]
=4R[cos
2
C
(sin
2
A
cos
2
B
+sin
2
B
cos
2
A
)−sin
2
C
(cos
2
A
cos
2
B
−sin
2
A
sin
2
B
)]
=4R[cos
2
C
sin
2
A+B
−sin
2
C
cos
2
A+B
]=4R[cos
2
C
sin(
2
π
−
2
C
)−sin
2
C
cos(
2
π
−
2
C
)]
=4R[cos
2
C
cos
2
C
−sin
2
C
sin
2
C
]=4RcosC
Answered By
toppr
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