Suppose you have a triangle ABC with an incircle centered at I, with inradius r and circumradius R. Let BC be denoted by a. Prove that the area of triangle DIE is given by the formula: \(S_1 = \dfrac{a\cdot r^2}{4\cdot R}\).
Suppose a triangle ABC you behold, With incircle
at I, inradius r to hold, And circumradius R, let BC
be denoted a, Prove that area of triangle DIE is no
cliche.
With formulas, proofs, and geometric lines, This
calculation, no longer one that confines, But reveals the
beauty of triangle centers, A world of shapes, geometry
adventure.
Oh, r is the inradius, and R, circumradius, The
calculation's elegance, enough to impress, And through this
math, a deeper meaning revealed, The intricate patterns of
shapes unconcealed.
So let us embrace, with wonder and delight, The secrets
geometry brings to light.
