If A,B, and C lie on a circle, then the center of the circle is the point of intersection of the perpendicular-bisectors of line AB and line BC.
2007-08-04 14:14:00 · 8 answers · asked by ½ÃÂù ± 2 in Science & Mathematics ➔ Mathematics
TRUE
[Explanation-Let O be the point of intersection of the two perpendicular bisectors AB and BC
As O lies on the perpendicular bisector of AB,it is equidistant from A ans B,i.e OA=OB
again as O lies on the perpendicular bisector of BC,it is equidistant from B and C
i.e.OB=OC
Therefore,OA=OB=OC
Therefore O is the centre of the circle drawn touching the three points A,B andC]
2007-08-04 14:16:48 · answer #1 · answered by alpha 7 · 3⤊ 0⤋
True. Each perpendicular bisector is a diameter of the circle (think about the isosceles triangle ABO, where O is the centre of the circle). So they necessarily pass through the centre. As long as A, B and C are distinct, the perpendicular bisectors will be distinct, and their point of intersection can only be the centre.
2007-08-04 21:20:10 · answer #2 · answered by SV 5 · 2⤊ 0⤋
Yes. All points on the _|_ bisector of AB are equidistant from the points A and B. All points on the _|_ bisector of BC are equidistant from the points B and C. Therefore their intersection is equidistant from points A,B,and C and therefore must be the center of the circle that passes through thee three points.
2007-08-04 21:25:48 · answer #3 · answered by ironduke8159 7 · 0⤊ 0⤋
It's true.
2007-08-04 21:16:58 · answer #4 · answered by 3.14 2 · 0⤊ 1⤋
sounds good to me.
I say true, but you get to prove it.
2007-08-04 21:23:57 · answer #5 · answered by trogwolf 3 · 1⤊ 1⤋
true
2007-08-04 22:20:31 · answer #6 · answered by mechnginear 5 · 0⤊ 0⤋
true
2007-08-04 21:23:06 · answer #7 · answered by CPUcate 6 · 0⤊ 1⤋
true!!!!!
2007-08-04 21:18:39 · answer #8 · answered by Anonymous · 0⤊ 2⤋