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In a triangle ABC, if r:r1 = r2:r3then which of the following are true?a^2 + b^2 + c^2=8R^2sin^2 A +sin^2 B + sin^2 C = 2a² +b² = c^2∆=s(s-a) |
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Answer» Step-by-step explanation: 1
=r 2
+r 3
+r⟹r 1
−r=r 2
+r 3
⟹SIN 2 A
cos 2 B
cos 2 C
−sin 2 A
sin 2 B
sin 2 C
=sin 2 B
cos 2 A
cos 2 C
−sin 2 C
cos 2 A
cos 2 B
⟹sin 2 A
(cos 2 B
cos 2 C
−sin 2 B
sin 2 C
)=cos 2 A
(sin 2 B
cos 2 C
−sin 2 C
cos 2 B
) ⟹sin 2 A
cos 2 (B+C)
=cos 2 A
sin 2 (B+C)
⟹tan 2 A
=tan 2 (B+C)
⟹A=B+C⟹2A=180 ∘ ⟹A=90 ∘ |
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