1. A(-3;4) is a point on a circle

Question

with centre at the origin.
a.determine the coordinates of B, if AB is a diameter.
b. Show that point C(0;5) lies on this circle.
c.show that ACB has a magnitude of 90degrees.

2.a.ddetermine the equation of the circle with AC as diameter, if A is the point (-5;12) and C(5;-12).
b.if B is the point (0;13) and D(-7;-2#30) show that ABCD is a cyclic quadrilateral, that all the vertices lie on the

Answer 1

#1
clearly the circle is of radius 5. So, since x^2+y^2 = 5^2, (0,5) lies on the circle.

the center is the midpoint of AC: (0,0)
so, the radius is 13.

0^2+13^2 = 13^2
7^2 + (2√30)^2 = 49+120 = 13^2

so, all vertices lie on the circle.