Question:
The vertices of a triangle are A(1, 1), B(0, 0) and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?
The vertices of a triangle are A(1, 1), B(0, 0) and C(2, 0). The angular bisectors of the triangle meet at P. What are the coordinates of P?
Options:
- a) (, )12 1-
- b) (, )13 1-
- c) 1 1 2,
- d) 1 2 21,
- a) (, )12 1-
- b) (, )13 1-
- c) 1 1 2,
- d) 1 2 21,
correct answer : a)
Explanation:
a = BC = () ()20 00 22-+ – = 2
b = AC = () ()21 01 22-+ – = 2
c = AB = () ()10 10 22-+ – = 2
\ Coordinate of incentive
=
ax bx cx
ab c
ay by cy
ab c
12 31 23++
++
++
++
,
= 21 20 22
22 2
21 20 20
22 2
() () () , () () ()++
++
++
++
=
22 2
22 2
2
22 2
+
++
, = 12 1 ,-()
a = BC = () ()20 00 22-+ – = 2
b = AC = () ()21 01 22-+ – = 2
c = AB = () ()10 10 22-+ – = 2
\ Coordinate of incentive
=
ax bx cx
ab c
ay by cy
ab c
12 31 23++
++
++
++
,
= 21 20 22
22 2
21 20 20
22 2
() () () , () () ()++
++
++
++
=
22 2
22 2
2
22 2
+
++
, = 12 1 ,-()