Question

Find the radius of the circle with centre at the origin if line (l) given by x + y = 5 is tangent to the circle at point P.

Answer 1

The line (l) is x + y = 5.

The tangent point is P(3, a).

Since P lies on the line, substitute into the equation:

3 + a = 5

a = 2

So the point of tangency is P(3, 2).

The centre of the circle is C(0, 0).

The radius is the distance:

CP = `sqrt((3 - 0)^2 + (2 - 0)^2)`

= `sqrt(3^2 + 2^2)`

= `sqrt(9 + 4)`

= `sqrt(13)` units