Question

In triangle ABC, \[ (r_1-r)\cos\frac{B-C}{2} = ? \]

• A. \((r_1+r)\sin\frac{A}{2}\)
• B. \((r_2+r_3)\sin\frac{A}{2}\)
• C. \((r_1+r)\sin\frac{B-C}{2}\)
• D. \((r_2+r_3)\sin\frac{B-C}{2}\) \bigskip

Hint:

For triangle geometry questions involving inradius and exradii, remember the important identity \[ (r_1-r)\cos\frac{B-C}{2} = (r_1+r)\sin\frac{A}{2}. \] Similar identities exist cyclically for \(r_2\) and \(r_3\). These are frequently asked in JEE Main and Advanced geometry problems.

Answer 1

The Correct Option is A