Question:
In \( \Delta ABC \), if \( \angle C = 90^\circ \), then \( \left( \frac{I_1 - I_3}{I_1} \right) \left( \frac{I_2 - I_3}{I_2} \right) = \):
In \( \Delta ABC \), if \( \angle C = 90^\circ \), then \( \left( \frac{I_1 - I_3}{I_1} \right) \left( \frac{I_2 - I_3}{I_2} \right) = \):
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In right-angled triangles, use specific properties of the incenter and excircles to simplify equations involving them.
Updated On: May 15, 2025
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The Correct Option is D
Solution and Explanation
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.
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