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02 Nov 2022, 01:05
Kudos
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Asked: Given the two lines y = 2x + 5 and y = 2x - 10, what is the area of the largest circle that can be inscribed such that it is tangent to both lines
Distance from point (0,0) to line {2x - y + 5 = 0 } = \(5/\sqrt{5} = \sqrt{5}\)
Distance from point (0,0) to line {2x - y - 10 = 0} = \(10/\sqrt{5} = 2\sqrt{5}\)
Distance between the 2 parallel lines = \(\sqrt{5}+ 2\sqrt{5}= 3\sqrt{5}\)
= Diameter of the circle
Radius of the circle = \(3\frac{\sqrt{5}}{2}\)
Area of the largest circle =\( \frac{45}{4}*\pi\)
IMO A
Distance from point (0,0) to line {2x - y + 5 = 0 } = \(5/\sqrt{5} = \sqrt{5}\)
Distance from point (0,0) to line {2x - y - 10 = 0} = \(10/\sqrt{5} = 2\sqrt{5}\)
Distance between the 2 parallel lines = \(\sqrt{5}+ 2\sqrt{5}= 3\sqrt{5}\)
= Diameter of the circle
Radius of the circle = \(3\frac{\sqrt{5}}{2}\)
Area of the largest circle =\( \frac{45}{4}*\pi\)
IMO A
13 Aug 2024, 14:03
Kudos
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