The area of circle circumscribing ΔABC is

Engineering

Mathematics

Basic Rules of Properties of Triangle

Question

$\frac{π}{4}$

$\frac{π}{2}$

$\frac{π}{8}$

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Angles BEC, ABD, ABE and BAC are in A.P.

let BEC = α – 3β

ABD = α – β

ABE = α + β

and BAC = α + 3β

now, α – 3β = (α + 3β) + (α + β) [using exterior angle theorem]

⇒ α = –7β

$β = - \frac{π}{24}, α = \frac{7 π}{24}$

and From ΔABD

$α - β + α + 3 β = \frac{π}{2}$

$2 β + 2 β = \frac{π}{2} \Rightarrow α + β = \frac{π}{4}$

∠B = 2(α + β) = $\frac{π}{2}, ∠ A = \frac{π}{6}, ∠ C = \frac{π}{3}$

ABC is 30°–90°–60° triangle

Area of circle circumscribing ΔABC = $π {(\frac{1}{2})}^{2} = \frac{π}{4}$

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