The plan is provided with an orthonormal reference ( O.I.J). the following points are given A(1,2) B(−2,3) C(1,9). We assume that the point O is the barycenter of the point A,B,C. →O=bar{(A;3),(B;1),(C;−1)} Question 1 knowing that 3MA^2 +MB^2 −MC^2 =3MO^2 +3OA^2 +OB^2 −OC^2 Determine and construct the set of points M on the plane such as 3MA^2 +MB^2 −MC^2 =−42


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Question Number 77356 by mathocean1 last updated on 05/Jan/20
$The plan is provided with an orthonormal reference ( O.I.J). the following points are given A(1,2) B(−2,3) C(1,9). We assume that the point O is the barycenter of the point A,B,C. →O=bar{(A;3),(B;1),(C;−1)} Question 1 knowing that 3MA^2 +MB^2 −MC^2 =3MO^2 +3OA^2 +OB^2 −OC^2 Determine and construct the set of points M on the plane such as 3MA^2 +MB^2 −MC^2 =−42$
$The plan is provided with an$ $orthonormal reference (O . I . J) .$ $the following points are given$ $A (1, 2) B (- 2, 3) C (1, 9) .$ $We assume that the point O is the$ $barycenter of the point A, B, C .$ $\to O = bar {(A; 3), (B; 1), (C; - 1)}$ $Question 1$ $knowing that$ ${3 MA}^{2} + {MB}^{2} - {MC}^{2} = {3 MO}^{2} + {3 OA}^{2} + {OB}^{2} - {OC}^{2}$ $Determine and construct the set$ $of points M on the plane such as$ ${3 MA}^{2} + {MB}^{2} - {MC}^{2} = - 42$
	Answered by mind is power last updated on 05/Jan/20

	${3 MA}^{2} + {MB}^{2} - {MC}^{2} = {3 MO}^{2} + {3 OA}^{2} + {OB}^{2} - {OC}^{2} = - 42$ ${OA}^{2} = 5, {OB}^{2} = 13, {OC}^{2} = 82$ $\Leftrightarrow {3 MO}^{2} + 3 (5) + 13 - 82 = - 42$ $\Leftrightarrow {MO}^{2} = 12 \Rightarrow MO = \sqrt{12} = 2 \sqrt{3}$ $M \in Circle center O Radius 2 \sqrt{3}$
	Commented by mathocean1 last updated on 05/Jan/20

	$thank you sir .$
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