Question

In the adjoining figure if AB = 8 cm BC = 6 cm AC = 10 cm then find the perimeter of the incircle .

binn faltu ka kuch likhna matt.. aata hoga tho ans dena ..​

Answer 1

Step-by-step explanation:

Let us suppose ABC be the equilateral triangle inscribed in a circle of radius r and centered at point O.

Draw perpendicular OD that meets the base BC at D.

Hence, BD = 7.5 cm.

Since, the radius of the triangle bisects the angle B. Hence, we have

\angle OBD = 30^{\circ}∠OBD=30

∘

In right angle triangle OBD, we have

\begin{gathered}\cos 30^{\circ} = \frac{7.5}{r} \\\\r=\frac{7.5}{\cos 30^{\circ} } \\\\r=5\sqrt3\end{gathered}

cos30

∘

=

r

7.5

r=

cos30

∘

7.5

r=5

3

Therefore, the area of the circle is given by

\begin{gathered}A=\pi r^2\\\\A=3.14(5\sqrt3)^2\\\\A=235.6 cm^2\end{gathered}

A=πr

2

A=3.14(5

3

)

2

A=235.6cm

2