InterviewSolution
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InterviewSolution
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Find the co-ordinates of the circumcenter of the triangle whose vertices are (8,6),(8.-2)and (2-2) |
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Answer» Let the coordinates of the circumcentre of the triangle be (x, y).Circumcentre of a triangle is equidistant from each of the vertices.Distance between (8, 6) and (x, y) = Distance between (8, -2) and (x, y)√[(x - 8)²+ (y - 6)²] = √[(x - 8)²+ (y + 2)²][(x - 8)²+ (y - 6)²] = [(x - 8)²+ (y + 2)²](y - 6)2= (y + 2)²y²+ 36 - 12y = y²+ 4y + 436 - 12y = 4y + 416y = 32y = 2Distance between (2, -2) and (x, y) = Distance between (8, -2) and (x, y)√[(x - 2)2+ (y + 2)2] = √[(x - 8)²+ (y + 2)²][(x - 2)²+ (y + 2)²] = [(x - 8)2+ (y + 2)²](x - 2)²= (x - 8)²x2+ 4 - 4x = x2- 16x + 644 - 4x = -16x + 6412x = 60x = 5.Hence, the coordiantes of the circumcentre of the triangle are (5, 2).Circumradius = √[(5 - 8)²+ (2 - 6)²]= √(9 + 16)= √25= 5 units. Please like the solution 👍 ✔️ |
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