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Question: If the straight lines 2x + y + 5 = 0 and 4x + 2y + 15 = 0 are the tangents to a circle, then radius ...

If the straight lines 2x + y + 5 = 0 and 4x + 2y + 15 = 0 are the tangents to a circle, then radius of this circle is

A

52\frac{\sqrt{5}}{2}

B

5\sqrt{5}

C

54\frac{\sqrt{5}}{4}

D

None of these

Answer

54\frac{\sqrt{5}}{4}

Explanation

Solution

Distance b/w || is equal to diameter of the circle

2r = ∣5–152∣4+1\frac{\left| 5–\frac{15}{2} \right|}{\sqrt{4 + 1}} ή 2r = 525\frac{5}{2\sqrt{5}} ή r = 54\frac{\sqrt{5}}{4} ή r = 54\frac{\sqrt{5}}{4}