00:00Here I am giving the vertices of the triangle in the question, that is, I am giving the coordinates of the corner of the triangle.
00:05Is
00:06The coordinate of A is 2,0,0, the coordinate of B is 0,6,0 and the coordinate of C is 0,0,4.
00:16A, D, B, E, C, F are medium
00:18That is, this D is at the midpoint of B, C, A, E is at the midpoint of A, C, and
00:26F is the midpoint of A, B
00:28And we're asked its value, A, D, squared plus B, squared plus F, squared
00:33So what we will do is, first of all there is a formula to find the midpoint.
00:37That is, X1 plus X2 upon me 2,Y1 plus Y2 upon me 2,Z1 plus Z
00:45upon me 2
00:47This will give the X, Y, and Z coordinates of the midpoint.
00:51So assuming this we will first find the coordinates of F, D and E
00:55coordinate of F, F between A and B, that is A plus B upon me 2, 2 plus
01:000 upon me 2.1
01:016 plus 0 upon me 2,3, 0 plus 0 upon me 2,0
01:06Similarly, the coordinate of E is, in the same way, the midpoint of A and C, that is, it becomes 1
01:13In Fibad it's 0, 4 plus 0 upon me 2, 2
01:18Similarly, now we will find the coordinate of D, B plus C upon me 2,0
01:226 plus 0 upon me 2,3, 0 plus 4 upon me 2,2
01:27Next are the coordinates of F, E, O, D, now just find the distance.
01:31Will apply the formula, under root X2-X1 square plus Y2-Y1 square plus Z2-Z1 square
01:40So let's apply the formula, then in the following, let's find the coordinates of E, D.
01:47First, 0-2, that is, minus 2, is the square under root of 4, plus 3-0, that is, 3.
01:57square 9, plus the square of Y2-0, that is, 2 squared is 4, so this is in my foot, under
02:09root 17,
02:11The value of AD, similarly the value of BE, so in the end, we will subtract BE from one, 1
02:18-0 ka, Isukaya, BE is equal to,
02:251 plus, this is 0-6, Isukaya, 36, plus 2-0, Isukaya, that is 2, Isukaya, 4, so
02:39It became, under the root of,
02:4241, The value of SACF, CF is equal to, under root, this, 1-0 of, Isukaya, 1, plus 3-0 of,
02:53Isukaya, means 3, Isukaya, 9,
02:56plus 0-4 of, Isukaya, that is, 4 of, Isukaya, 16, this, becomes, under root, 16, plus 9, 25,
03:05Ban 26, now Amen,
03:19This, 8 would go on doing, basically, 40, plus 20, that's it, 60, plus 10, 70, 77, 78, 78, 78, plus 6,
03:3384,
03:33So, this, Samha, in Mare Pat, further, 84, so, its answer will be Ajaega,
03:38Final Answer, 84, Answer,
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