Question

Show that the points (-8, 5, 2) (-5, 2, 2) (-7,6,6) (-4,3,6) are concyclic​

Answer 1

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.