It's staring at me

Let ΔABC\Delta ABC be a triangle with vertices A=(0,0),B=(6,0),C=(3,33), A=(0,0), B=(6,0), C=\big(3,3\sqrt{3}\big), and ΔPQR\Delta PQR the pedal triangle of ΔABC.\Delta ABC.

The sum of the circumradius of ΔABC \Delta ABC and inradius of ΔPQR \Delta PQR can be expressed as abc\frac{a\sqrt{b}}{c} for positive integers a,b,a,b, and c,c, where a,ca,c are coprime and bb is square-free.

Find a×b×ca\times b\times c.

×

Problem Loading...

Note Loading...

Set Loading...