InterviewSolution
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InterviewSolution
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IfA(2,2), B(-2, -2) , C(-2sqrt(3), 2sqrt(3)) and D(-4-2sqrt(3), 4+2sqrt(3)) are the co-ordinates of 4 points. What can be said about these four points ? |
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Answer» Solution :`""AB=sqrt((-2-2)^(2)+(-2-2)^(2))=4sqrt(2)` units `""BC=sqrt((-2+2sqrt(3))^(2)+(-2-2sqrt(3))^(2))` `""=sqrt (4+12-8sqrt(3)+4+12+8sqrt(3))=4sqrt(2) ` units `""CD=sqrt((-2sqrt3+4+2sqrt(3))^(2)+(2sqrt(3)-4-2sqrt(3))^(2))` ` "" =sqrt(16+16)=4sqrt(2)` units `""AC=sqrt((2+2sqrt(3))^(2)+(2- 2sqrt(3))^(2))` `""=sqrt(4+12+8sqrt(3)+4+12-8sqrt(3))=4sqrt(2)` units ` ""AD=sqrt((2+4+2sqrt(3))^(2)+(2-4-2sqrt(3))^(2))` `""=sqrt(36+12+24sqrt(3)+12+4+8sqrt(3))=sqrt(64+32sqrt(3))` units `""BD=sqrt((-2+4+2sqrt(3))^(2)+(-2-4-2sqrt3)^(2))` `""=sqrt(4+12+8sqrt(3)+36+12 +24sqrt(3))=sqrt(64+32sqrt( 3))` units Here, `AB =BC=CD=AC` and also, `AD=BD` So, in first view it SEEMS to be the vertices of a square. `""BUT""` Here, ` AB, BC, CD and DA` are not equal. (order of `A, B, C and D` must be cyclic in case of square). Also AD and BD are equal but they cannot be the DIAGONALS. So, they do not form a square. Actually, A, B and D lie on a circle with C as the CENTRE (as CA=CB=CD i.e., C is equidistant from A, B and D). |
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