If `A(0, 0), B(1, 0) and C(1/2,sqrt(3)/2)` then the centre of the circle for which the lines `AB,BC, CA` are tangents is

Question

If `A(0, 0), B(1, 0) and C(1/2,sqrt(3)/2)` then the centre of the circle for which the lines `AB,BC, CA` are tangents is

If `A(0, 0), B(1, 0) and C(1/2,sqrt(3)/2)` then the centre of the circle for which the lines `AB,BC, CA` are tangents is
A. `((1)/(2),(1)/(4))`
B. `((3)/(2),(sqrt3)/(2))`
C. `((1)/(2),(1)/(2sqrt3))`
D. `((1)/(2),-(1)/(sqrt3))`

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
`AB=AC=BC=1`
So, triangle is an equilateral.
Thus, incentre coincide with centroid.
Centre of the circle touching all the three sides of triangle is incentre.
therefore, incentre is
`((0+1+(1)/(2))/3,(0+0+(sqrt3)/(2))/3)=((1)/(2),(1)/(2sqrt3))`

4 views Answered 2023-02-05 15:29