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Need to calculate the radius of the circle, which is tangent to three lines with a given angle.

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José Carlos Santos
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Silambuselvan Thangaraj
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  • Some of the answers here give good hints: https://math.stackexchange.com/questions/656497/find-a-circles-radius-with-three-known-tangent-lines – David K Jun 28 '19 at 12:44

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Hint: draw the radius of the circle, from the centre to the contact points. Use symmetry. You'll find the equation $$ \tan{\frac{99^{\circ}}{2}} = \frac{R}{\left( 5/2 \right)} $$

Matti P.
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  • It may help make the result clearer if you also draw the line segments that connect the center of the circle to the intersections of the lines (that is, to the two ends of the segment of length $5$). – David K Jun 28 '19 at 12:45