In an isoscles triangle, we can find the radius of the incircle by using the fact that the angle bisector of the third (unequal) angle is the perpendicular bisector of the third(not equal) side and acts as a median and the other two angle bisectors are medians too. However, can we find the area of any one of the three sections of the triangle is divided into?( excluding the circle) ( please refer to the image)
Of course we can find the sum of the areas of the three sections by subtracting the area of the circle from the area of the triangle.
1.) From $BX = 0.5y$ and $IX = r$, find the area of $BXIY$ ($=m$, say).
2.). Find $\alpha$. From which, deduce $\beta$ and then $\delta$.
3.) Find the area of the blue sector ($=n$, say).
4.) Area of region $b = m + n - \pi r^2$