Question

The radius of a circle with centre(2,2) and a point on the circle (2,5)​

Answer 1

Step-by-step explanation:

Given: centre of the circle (2, 2)=(h, k)

Point on the circle (2, 5) = (x, y)

Equation of circle in centre radius form is given as:

$(x - h)^{2} + (y - k)^{2} = {r}^{2} \\ \therefore \: (2 - 2)^{2} + (5 - 2)^{2} = {r}^{2} \\ \therefore \: (0)^{2} + (3)^{2} = {r}^{2} \\ \implies \: 0 + 9 = {r}^{2} \\ \implies \: {r}^{2} = 9 \\ \implies \: {r} = \sqrt{9} \\ \implies \: {r} = 3 \: units \:$

Thus the radius of the circle is 3 units.