## Solutions of Triangles — a tricky IITJEE problem

**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

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