Turkish NMO First Round - 1999 P-05 (Geometry)
Source:
July 3, 2012
geometry
Problem Statement
Let be an isosceles triangle with \left|AB\right| \equal{} \left|AC\right| \equal{} 10 and \left|BC\right| \equal{} 12. and are points on such that \left|BP\right| \equal{} \left|RC\right| \equal{} 3. and are midpoints of and , respectively. If and are the foot of perpendiculars from and to , then find . (A)\ \frac {9\sqrt {13} }{26} \qquad(B)\ \frac {12 \minus{} 2\sqrt {13} }{13} \qquad(C)\ \frac {5\sqrt {13} \plus{} 20}{13} \qquad(D)\ 15\sqrt {3} \qquad(E)\ \frac {10\sqrt {13} }{13}