Dynamic Geometry: P99

Geometry Level 5

The diagram shows a black semicircle with radius 11. The cyan and green semicircle are growing and shrinking freely on the black semicirle's diameter. The purple circle is internally tangent to the black semicircle and tangent to both green and cyan semicircle. The red and orange circles are internally tangent to the black semicircle and tangent to the purple circle and to one of the bottom semicircles. The tangency points between the orange circle, the red circles and the purple circle trace a locus (blue curve). The area bounded by the blue curve and the black semicircle's diameter can be expressed as:

pqtan1(m)nm\frac{p}{q}\tan ^{-1}\left(m\right)-\frac{n}{m}

where pp, qq, mm and nn are positive integers. pp and qq are coprime. mm and nn are prime. Find p+q+m+np+q+m+n.

×

Problem Loading...

Note Loading...

Set Loading...