Have a circle with a radius of 1. Split the circle into 4 equal quadrants. Inside 1, draw a circle that touches both radius and the circle arc. How do I calculate the radius of smaller circle ?

Cheers

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- Nov 3rd 2012, 12:26 AMArchiecrabCircle problem
Have a circle with a radius of 1. Split the circle into 4 equal quadrants. Inside 1, draw a circle that touches both radius and the circle arc. How do I calculate the radius of smaller circle ?

Cheers - Nov 3rd 2012, 01:38 AMearbothRe: Circle problem
- Nov 3rd 2012, 02:06 AMMarkFLRe: Circle problem
I used an identical drawing and determined the point where the two circles touch must have equal coordinates, and so we may determine:

And thus we may state:

After simplification we find:

- Nov 3rd 2012, 06:34 AMHallsofIvyRe: Circle problem
And, remarkably, those two answers are the same!

Starting with earboth's result, , multiply both numerator and denominator by 2 to get . Now, "rationalize" the denominator by multiplying both numerator and denominator by :