If where r = 1,2,3 be the co-ordinates of the points A, B, C respectively, then prove the following:
The equation of internal bisector of angel A is
$b ∣ ∣ x x_{1} x_{2} y y_{1} y_{2} 111 ∣ ∣ + c ∣ ∣ x x_{1} x_{3} y y_{1} y_{3} 111 ∣ ∣ = 0$
where b = AC and c = AB.

Question

If where r = 1,2,3 be the co-ordinates of the points A, B, C respectively, then prove the following:
The equation of internal bisector of angel A is

b ∣ ∣ x x_{1} x_{2} y y_{1} y_{2} 111 ∣ ∣ + c ∣ ∣ x x_{1} x_{3} y y_{1} y_{3} 111 ∣ ∣ = 0

where b = AC and c = AB.

Filo · Accepted Answer

In this case if AD be the internal bisector it will divide the opposite side BC in the ratio of the arms of the angel i.e. AB : AC or c : b

∴ D i s (\frac{c x _{3} + b x _{2}}{c + b}, \frac{c y _{3} + b y _{2}}{c + b})

Then, as above, on applying the condition of collinearly

∣ ∣ x x_{1} \frac{c x _{3} + b x _{2}}{c + b} y y_{1} \frac{c y _{3} + b y _{2}}{c + b} 111 ∣ ∣

Multiply

R_{3}

by c + b and split into two determinants.

Question Text	If where r = 1,2,3 be the co-ordinates of the points A, B, C respectively, then prove the following: The equation of internal bisector of angel A is $b ∣ ∣ x x_{1} x_{2} y y_{1} y_{2} 111 ∣ ∣ + c ∣ ∣ x x_{1} x_{3} y y_{1} y_{3} 111 ∣ ∣ = 0$ where b = AC and c = AB.
Answer Type	Text solution:1
Upvotes	150

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