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Question: The line 2x – y + 1 = 0 is tangent to the circle at the point (2, 5) and the centre of the circle l...

The line 2x – y + 1 = 0 is tangent to the circle at the point

(2, 5) and the centre of the circle lies on x –2y = 4. The radius of the circle is:

A

353 \sqrt { 5 }

B

535 \sqrt { 3 }

C

252 \sqrt { 5 }

D

525 \sqrt { 2 }

Answer

353 \sqrt { 5 }

Explanation

Solution

Let centre is (4 + 2B, B);

r = = (2B +2)2 + (5 –B)2 ; B = 1

Centre (8, 2), Radius = 353 \sqrt { 5 }