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In a ∆ABC, A(4,-1) and internal angle bisectors of B and C are x-y=1 and 2x-y=3. Find the inradius. Thanks.

In a ∆ABC, A(4,-1) and internal angle bisectors of B and C are x-y=1 and 2x-y=3. Find the inradius.
Thanks.

Grade:11

1 Answers

Aaryan Daksh
28 Points
3 years ago
First of all draw a diagram.
Given two bisectors are x-y=1 and 2x-y=3.
On solving this we get the points (2,1)
This will become the centre of the internal circle.
 
(2,1) lies on line x-y=1.Slope of line is 1.
Now the side of triangle with vertices (4,-1) will become tangent to the given circle whose slope will be -1. The eqn. of line with point (4,-1) and slope =-1 will be x+y+3=0.
 
Finally use perpendicular distance formula for line x+y+3=0 and point (2,1) to find the radius.
 
The answer will be 3√2.
I hope this is correct 🤔
 
The answer will be 3√2.
I hope this is correct 🤔

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