Question

The line 2x−y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x−2y=4 . Then find the radius of the circle.

Answer 1

Answer:

Given:

Tangent, T:2x−y+1=0

Slope of tangent, T to the circle is 2

The line joining the centre and the point of contact of tangent is perpendicular with the tangent.

Thus, slope of line OA=−

2

1

Equation of OA,

(y−5)=−

2

1

(x−2)

x+2y=12

∴ Intersection with x−2y=4 will give coordinates of centre which are (8,2)

∴r=OA=

(8−2)

2

+(2−5)

2

=3

5

Hence, option A.

solution