If `Delta` represents the area of acute angled triangle ABC `sqrt(a^(2)b^(2) -4Delta^(2)) + sqrt(b^(2) c^(2) -4Delta^(2)) + sqrt(c^(2) a^(2) -4Delta^(

Question

If `Delta` represents the area of acute angled triangle ABC `sqrt(a^(2)b^(2) -4Delta^(2)) + sqrt(b^(2) c^(2) -4Delta^(2)) + sqrt(c^(2) a^(2) -4Delta^(

If `Delta` represents the area of acute angled triangle ABC `sqrt(a^(2)b^(2) -4Delta^(2)) + sqrt(b^(2) c^(2) -4Delta^(2)) + sqrt(c^(2) a^(2) -4Delta^(2))=`
A. `a^(2)+ b^(2) + c^(2)`
B. `(a^(2) + b^(2) + c^(2))/(2)`
C. `ab cos C + bc cos A + ca cos B`
D. `ab sin C + bc sin A + ca sin B`

Monjur Alahi

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2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - B::C
`2Delta = ab sin C rArr a^(2)b^(2) - 4Delta^(2) = a^(2) b^(2) cos^(2)C`
`rArr sqrt(a^(2) b^(2) - 4Delta^(2)) + sqrt(b^(2) c^(2) -4Delta^(2)) + sqrt(c^(2) a^(2) - 4 Delta^(2))`
`= ab cos C + bc cos A + ca cos B`
`= (a^(2) + b^(2) + c^(2))/(2)` (using cosine rule)

5 views Answered 2023-02-05 15:29