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If the incircle of the Delta ABC touches...

If the incircle of the `Delta ABC` touches its sides at `L`, `M` and `N` as shown in the figure and if `x`, `y`, `z` be thecircumradii of the triangles `MIN`, `NIL` and `LIM` respectively, where `I` is the incentre, then the product `xyz` is equal to:
(A) `R r^2`         (B)` r R^2`
(C) `1/2R r^2 `         (D) `1/2r R^2`

Text Solution

AI Generated Solution

To solve the problem, we need to find the product \( xyz \) where \( x, y, z \) are the circumradii of triangles \( MIN, NIL, \) and \( LIM \) respectively, and \( I \) is the incenter of triangle \( ABC \). ### Step-by-Step Solution: 1. **Understanding the Configuration**: - The incircle of triangle \( ABC \) touches the sides at points \( L, M, \) and \( N \). - The angles at the incenter \( I \) are important for finding the circumradii of the smaller triangles. ...
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