Question

If R is the circum radius of Δ ABC, then A(Δ ABC) = ______.

विकल्प

• \[\frac{\text{abc}}{\text{R}}\]

• \[\frac{\text{abc}}{\text{4R}}\]

• \[\frac{\text{abc}}{\text{3R}}\]

• \[\frac{\text{abc}}{\text{2R}}\]

Answer 1

If R is the circum radius of Δ ABC, then A(Δ ABC) = \[\underline{\frac{\text{abc}}{\text{4R}}}\].

Explanation:

In any Δ ABC we know that

Area of Δ = `1/2` bc sin A

`=> sin "A" = (2Delta)/"bc"`    ...(i)

also, R = `"a"/(2 sin "A")`    ...(ii)

From Eqs. (i) and (ii), we have

R = `"a"/(2((2Delta)/"bc"))`

`=> "R" = "abc"/(4Delta)`

`=> Delta = "A"(Delta "ABC") = "abc"/"4R"`