The figure below shows a triangle ABC with the circumradius R, the inradius r. If \(d, e, f\) are the distances from the midpoints of arcs AB, AC, BC to the sides BC, BC, and AC, respectively, prove that \(d+e+f=2(R+r)\).

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Geometry Problems

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Ten problems: 1411-1420

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Triangle

Circle

Triangle Centers

Circumradius, Circumcenter

Inradius, Incenter, Incircle

Midpoint

Perpendicular lines

Circle Tangent Line

Dynamic Geometry

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HTML5 and Dynamic Geometry

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