What-is-the-area-of-eqilateral-triangle-whose-inscribed-circle-has-a-radius-2-

Question Number 12743 by tawa last updated on 30/Apr/17

What is the area of eqilateral triangle whose inscribed circle has a radius 2

Answered by mrW1 last updated on 30/Apr/17

O C = 2

O B = 4 = D O

C B = 2 \sqrt{3}

D C = 4 + 2 = 6

A B = 2 \times 2 \sqrt{3} = 4 \sqrt{3}

A_{A B C} = \frac{1}{2} \times 4 \sqrt{3} \times 6 = 12 \sqrt{3}

o r

A_{A B C} = 6 \times A_{O C B} = 6 \times \frac{1}{2} \times 2 \sqrt{3} \times 2 = 12 \sqrt{3}

Commented by mrW1 last updated on 30/Apr/17

Commented by tawa last updated on 30/Apr/17

God bless you sir .

Answered by b.e.h.i.8.3.4.1.7@gmail.com last updated on 30/Apr/17

s = {n r}^{2} t a n \frac{π}{n} = 3 \times 4 \times t g \frac{π}{3} = 12 \sqrt{3} .

Commented by tawa last updated on 30/Apr/17

God bless you sir

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