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Question

The vertices of a triangle are A(0,6), B(6,0) and C(1,1) respectively. Then coordinates of the excentre opposite to vertex A are

A
(32,32)
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B
(4,32)
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C
(32,32)
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D
(4,6)
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Solution

The correct option is D (4,6)
a=BC=(61)2+(01)2a=50=52
b=CA=(10)2+(1+6)2b=50=52
c=AB=(0+6)2+(60)2c=72=62

Coordinates of excentre opposite to vertex A
x=ax1+bx2+cx3a+b+cx=520+52(6)+62(1)52+52+62x=24262=4

y=ay1+by2+cy3a+b+cy=52(6)+520+62(1)52+52+62y=36262=6

Hence, the coordinates of the excentre opposite to vertex A are (4,6).

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