Question

Show that the points p(7,12) and q(-3,-12) and r (14,5) lie on a circle with center c(2,0)

Answer 1

If the points P (7, 12), Q (-3, -12) and R (14, 5) lie on a circle with the center C (0, 2), then the distance OP, OQ and OR are the same.

The formula of a distance between two points:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Substitute:

`OP=√((2-7)^2+(0-12)^2)=√((-5)^2+(-12)^2)=√(25+144)=√(169)\\\\\boxed{OP=13}\\\\OQ=√((2-(-3))^2+(0-(-12))^2)=√(5^2+12^2)=√(25+144)=√(169)\\\\\boxed{OQ=13}\\\\OR=√((2-14)^2+(0-5)^2)=√((-12)^2+(-5)^2)=√(144+25)=√(169)\\\\\boxed{OR=13}`

OP = OQ = OR, therefore the points P, Q and R lie on one circle.