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Excenters of Triangle - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

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ABC is an equilateral triangle such that the vertices B and C lie on two parallel lines at a distance 6. If A lies between the parallel lines at a distance 4 from one of them then the length of a side of the equilateral triangle is

 

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Excenters of Triangle

Excenters of Triangle

An excenter is a point at which the line bisecting one interior angle meets the bisectors of the two exterior angles on the opposite side.

The circle opposite to the vertex A is called the escribed circle or the circle escribed to the side BC . If I1 is the point of intersection of the internal bisector of ∠BAC and external bisector of ∠ABC and ∠ACB then,

Coordinates of I1 , I2 and I3 is given by

\\\mathrm{I_1\equiv \left(\frac{-a x_{1}+b x_{2}+c x_{3}}{-a+b+c}, \frac{-a y_{1}+b y_{2}+c y_{3}}{-a+b+c}\right)}\\\\\mathrm{I_2\equiv\left(\frac{a x_{1}-b x_{2}+c x_{3}}{a-b+c}, \frac{a y_{1}-b y_{2}+c y_{3}}{a-b+c}\right)}\\\\\mathrm{I_3\equiv\left(\frac{a x_{1}+b x_{2}-c x_{3}}{a+b-c}, \frac{a y_{1}+b y_{2}-c y_{3}}{a+b-c}\right)}

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Excenters of Triangle

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Circumcentre and Orthocentre
Incentre
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Locus
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Excenters of Triangle

Mathematics for Joint Entrance Examination JEE (Advanced) : Coordinate Geometry

Page No. : 1.14

Line : 49

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