The neighbouring sides AB and BC of a square ABCD of side ( 2 + 2 ) units are tangents to a circle. The vertex D of the square lies on the circumference of the circle. The radius of the circle is

Question

The neighbouring sides AB and BC of a square ABCD of side ( 2 + 2 ​ ) units are tangents to a circle. The vertex D of the square lies on the circumference of the circle. The radius of the circle is

TestHub · Accepted Answer

Let y = mx + c be the tangent to the given ellipse y = 2 x ± a 2 + 4 e + l 2 ​ Which passes the ( − 2 , 0 ) 4 a 2 + l 2 = 16 let s = al s 2 = a 2 l 2 = a 2 ( 16 − 4 a 2 ) s max ​ a t − a l ​ then l = 8 ​ Max. value of al = 4

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