A geometry problem by Matthew Tam
Geometry
Level
pending
Given a circle with radius 20, there are indefinetly many line segments of length 20 that are tangent to the circle at their midpoints. Find the area of the region consisting of all such line segments
90 pi
Jonathan Hsu should solve this
I think Andrew should as well
100 pi
83 pi
Indefinite
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1 solution
Area of given circle = pi r^2 = pi (20)^2 = 400 pi
Radius of a circle formed by many line segment of length 20 = (20^2 +10^2)^0.5 = 10(5)^0.5
Area of circle formed by many line segments= pi r^2= 500 pi
Area of region consisting all such lines = 500 pi - 400 pi = 100 pi (Ans.)