Question (IITJEE 1978). Suppose are the altitudes through vertices A, B, C of a triangle ABC with area
.
Prove that:
Proof:
The RHS looks daunting. But, if we bring the factor in its denominator to the LHS, then the problem unfolds itself. Since,
, the problem is equivalent to the following:
prove:
If we write as
, and multiply both the sides of by
, then the problem is reduced to proving that
.
which is the same as the cosine formula 🙂 🙂 🙂
More later…
Nalin Pithwa