(a) For a triangle ABC, show that
(i) AB is perpendicular to BC
(ii) BM = CM, where M is the midpoint of AC
(b) Find also an equation of circle passing through A, B & C
(b)
the equation of the circle is (x-h)^2 + (y-b)^2 = r^2
where (h,x) is the midpoint of the circle and r = radius of the circle
substitute the values of A (1,3) in the place of (x,y) in the equation..
like this
(1-h)^2 + (3-b)^2 = r^2
do the same with points B and C
with B : (5-h)^2 +(9-b)^2 = r^2
with C : (8-h)^2 + (7-b)^2 - r^2
the radius of the circle is the same
therefore all the equations above should be equal
(1-h)^2 + (3-b)^2 = (5-h)^2 + (9-b)^2 = (8-h)^2 + (7-b)^2
rearrange them and you'll get one of the values of either h or B
then subsitute this value to get the other values
you'll get the midpoint of the circle
all you need is the radius now
so use one of the points example A which is (1,3)
(1-h)^2 +(3-b)^2 = r^2
to get it since you have the values of the midpoint (h,b) which u would've have obtained previously
