Question

Find the diameter of a circle whose centre is at (3,2) and passes through (10,26)

Answer 1

diameter = 50 units

Explanation:

the diameter(d) of a circle is twice the radius (r)

the radius is the distance from the centre to a point on the circle.

to calculate r use the distance formula

r =
`\sqrt{(x_(2)-x_(1))^2+(y_(2)-y_(1))^2 }`

with (x₁, y₁ ) = (3, 2 ) and (x₂, y₂ ) = (10, 26 )

r =
`√((10-3)^2+(26-2)^2)`

=
`√(7^2+24^2)`

=
`√(49+576)`

=
`√(625)`

= 25

Then

diameter d = 2 × r = 2 × 25 = 50 units