The arc along the arc

Geometry Level 4

The hemisphere is inscribed in the rectangle.

Note: You might have to enlarge the image to see the points x , y , z x, y, z defined in the diagram.

7.1 6.9 4.7 6.2

Charlston Redulosa by Charlston Redulosa , 31, Japan

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1 solution

Ajit Athle
Sep 9, 2014

I assumed the circle to be of unit radius. Angle A can be determined from the equation: 2tan(A)+2tan(A/2)=1. Thereafter we can write down the equation of the line and the circle and calculate the co-ordinates of X & Y, determine the length of XY and YZ. Scale up the figure to YZ = 3 and obtain the new length XY for YZ=3. The problem here that XY turns out to be 5.8 and not 6.2. Can the problem-setter please look into this?

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Are you referring to the arc length? X to y..?

Charlston Redulosa - 6 years, 6 months ago

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