Learned this one in 6th grade geometry: drawing a square in thr corner doesn't make it 90°
this post was submitted on 08 Jun 2025
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But these are all right angles, as long as the two arcs are centered on the same point as the intersection of the two straight lines.
drawing a square in thr corner doesn’t make it 90°
No, it doesn't, but it does mean that, for the purposes of your 6th grade geometry question, you can assume the angle is a right angle. Even if it visible looks like 45°, if they put a square there, that's 90.
More to the point though, a radius of a circle always meets the circumference at 90 degrees. All the squares in this problem are doing is telling you "this line, if it were continued, would be the radius of the incomplete circle".
Dammit Diogenes, this is why we don't allow you in the geometry class anymore.
Solution:
Explanation:
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in order for the straight lines to be 90 deg with the circles, they must be radii of circles with same central point
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the length of an arc is defined as c = r * θ (where r is the radius, and θ is the angle)
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we define the inner circle with radius r₁ and its arc L₁ = r₁ * θ₁
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we define the outer circle with radius r₂ and its arc L₂ = r₂ * θ₂
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Because of (1), θ₁ + θ₂ = 2π
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To create the shape, L₁ = L₂ = r₂ - r₁
If you start replacing and solving, you will get a 2nd grade quadratic, which has a positive and a negative solution. The positive solution is that magic number.
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