# Thread: midpoint of a cricle.

1. ## midpoint of a cricle.

Pls help me and guide me into solving this. My maths is weak so please explain to me step by step. Anyway this a a programming question. i just need steps to solve it. There is also a hint : using perpendicular line formula

Attempt solution/what i think : Using A & B to get m1 then using perpendicular formula, to get m2(at point D). Apply same method to get m at E. so now the two mD and mE will intersect at center. From here i am lost and how to find the center coords and the radius.

Thanks

2. ## Re: midpoint of a cricle.

Originally Posted by watsonmath

There is also a hint : using perpendicular line formula
Attempt solution/what i think : Using A & B to get m1 then using perpendicular formula, to get m2(at point D). Apply same method to get m at E. so now the two mD and mE will intersect at center. From here i am lost and how to find the center coords and the radius.
Let $A(x_a,y_a),~B(x_b,y_b),~\&~C(x_c,y_c)~$.
Then
$D:\left( {\frac{{x_a + x_b }}{2},\frac{{y_a + y_b }}{2}} \right)~\&~E:\left( {\frac{{x_c + x_b }}{2},\frac{{y_c + y_b }}{2}} \right)$

Now the slopes
$m_D=\left( { - \frac{{x_a - x_b }}{{y_a - y_b }}} \right)~\&~m_E=\left( { - \frac{{x_c - x_b }}{{y_c - y_b }}} \right)$.

3. ## Re: midpoint of a cricle.

Thanks i got it. So to continue, using y = mx + c , i sub x & y of D to get c to form straight line eqn(1) likewise for E to get eqn(2).
eqn(1) = eqn (2) Solve and substitute and i get the coordinate for center . Am i right ??

but how can i find the radius??

4. ## Re: midpoint of a cricle.

Originally Posted by watsonmath
how can i find the radius??
If $O$ is the center then the radius is the distance from $O \text{ to }A.$

5. ## Re: midpoint of a cricle.

Hi watsomath,
Without naming the coordinates A,B,C you cannot find a center coordinate or radius of the circumscribed circle