Question

In \( \Delta ABC \), if \( \angle C = 90^\circ \), then \( \left( \frac{I_1 - I_3}{I_1} \right) \left( \frac{I_2 - I_3}{I_2} \right) = \):

• A. 1
• B. 3
• C. 4
• D. 2

Hint:

In right-angled triangles, use specific properties of the incenter and excircles to simplify equations involving them.

Answer 1

The Correct Option is D

We are given a right-angled triangle where \( \angle C = 90^\circ \). Using the properties of the incenter and applying the standard formula for the incircles, we simplify the equation \( \left( \frac{I_1 - I_3}{I_1} \right) \left( \frac{I_2 - I_3}{I_2} \right) \) and obtain the value as 2.