Question

Find the Perimeter and the Area if the Triangle​

Answer 1

Answer:

Let the side of triangle be 2x . Triangles BAC and ADC are similar . So angle BAC will be 30° .

BC radius is perpendicular to tangent AB

Now

$\cos(30 ) = \frac{10}{x} \\ \\ x = 10 \times \frac{2}{ \sqrt{3} } = \frac{20}{ \sqrt{3} }$

So side of equilateral triangle

$= 2x = \frac{40}{ \sqrt{3} }$

And area

$= \frac{ \sqrt{3} }{4} {a}^{2} = \frac{ \sqrt{3} }{4} \times \frac{40 \times 40}{3} = \frac{400 \sqrt{3} }{3}$

Answer 2

400 root 3 / 3

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