# math

show that the points A(0,-4) B(3,-1) C(-3,-1) lie on the circle whose centre is (0,1). find the length of its radios

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1. r = [-4 -1] = 5.

A(0 , -4), B(3 , -1), C(-3 , -1).
CTR(h , k) = CTR(0 , 1).

CTR(0 , 1), B(3 , -1).
tanA = (-1 - 1) / (3 - 0) = -2/3 = -0.6666,
A = -33.7 = 326.3 CCW.
X = h + rcosA = 0 + 5cos326.3 = 4.16.

Y = k + rsinA = 1 + 5sin326.3 = -1.77.

Eq:(x - h)^2 + (y - k)^2 = r^2.
(x - 0)^2 + (y - 1)^2 = 25.

(4.16 - 0)^2 + (-1.77 - 1)^2 = 25.
Therefore, point B satisfies the Eq.

CTR(0 , 1), C(-3 , -1).
tanA = (-1-1) / (-3 - 0) = -2 / -3 = 0.6666,
A = 33.7 Deg.

X = 0 + 5cos33.7 = 4.16.

Y = 1 + 5sin33.7 = 3.77.

(4.16 - 0)^2 + (3.77 - 1)^2 = 25.
Therefore point C satisfies the Eq.

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posted by Henry

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