Question

How many units are in the length of the radius of the circle which passes through points X, Y, Z. Express your answer in simplest radical form.

Answer 1

Given : circle  passes through points X, Y, Z

To Find : Radius

Solution:

Let say O is the center of circle

draw OM ⊥ XZ  

as circle passes through X , Y &  Z Hence XZ is chord

OM ⊥ XZ

=> M i mid point of XZ

XZ = 8 + 12 = 20

=> XM = 10  

Let say OM = a

and radius = R  

OX = R

=> R² = 10²  + a²

OY = R

R² = (6 + a)²  + (10 - 8)²

(6 + a)²  + (10 - 8)² = 10²  + a²

=> 36 + a² + 12a + 4 = 100 + a²

=> 12a  = 60

=> a = 5

R² = 10²  + a²

=> R² = 100 + 25

=> R² = 125

=> R = 5√5  unit

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