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Show that the points (-8, 5, 2) (-5, 2, 2) (-7,6,6) (-4,3,6) are concyclic |
Answer» GIVEN:points- A(-8,5,2), B(-5,2,2), C(-7,6,6), D(-4,3,6) To find:Points are concyclic. Solution:For points to be concyclic, BD × AC = AD×BC + AB×DC by PUTTING all the given values, we can calculate √(-5-4)² + (2+3)² + (2+6)² × √(-8-7)² + (5+6)² + (2+6)² = √(-8-4)² + (5+3)² + (2+6)² × √(-5-7)² + (2+6)² + (2+6)² + √(-8-5)² + (5+2)² + (2+2)² × √(-7-4)² + (6+3)² + (6+6)² ∵ √81+25+64 ×√225+121+64 = √144+64+64 × √144+64+64 + √169+49+8 × √121+81+144 ∵ √170 × √410 = √272×√272 + √226×√346 ∵ √69700 = √73984 + √78196 ∵ 264.00 = 264.00 THEREFORE, the given points are concyclic.
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