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In A B C , the coordinates of the verte...

In ` A B C` , the coordinates of the vertex `A` are `(4,-1)` , and lines `x-y-1=0` and `2x-y=3` are the internal bisectors of angles `Ba n dC` . Then, the radius of the encircle of triangle `A B C` is (a) `4/(sqrt(5))` (b) `3/(sqrt(5))` (c) `6/(sqrt(5))` (d) `7/(sqrt(5))`

A

`4//sqrt(5)`

B

`3//sqrt(5)`

C

`6//sqrt(5)`

D

`7//sqrt(5)`

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The correct Answer is:
To solve the problem step-by-step, we will follow the instructions given in the video transcript and provide hints for each step. ### Step 1: Identify the given information We have the coordinates of vertex A as \( A(4, -1) \), and the equations of the angle bisectors as: 1. \( L_1: x - y - 1 = 0 \) 2. \( L_2: 2x - y - 3 = 0 \)
To solve the problem step-by-step, we will follow the instructions given in the video transcript and provide hints for each step. ### Step 1: Identify the given information We have the coordinates of vertex A as \( A(4, -1) \), and the equations of the angle bisectors as: 1. \( L_1: x - y - 1 = 0 \) 2. \( L_2: 2x - y - 3 = 0 \)
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