MathDB
2018 PUMaC Live Round 7.3

Source:

January 13, 2019
PuMACLive Round

Problem Statement

Kite ABCDABCD has right angles at BB and DD, and AB<BCAB<BC. Points E∈ABE\in AB and F∈ADF\in AD satisfy AE=4AE=4, EF=7EF=7, and FA=5FA=5. If AB=8AB=8 and points XX lies outside ABCDABCD while satisfying XE−XF=1XE-XF=1 and XE+XF+2XA=23XE+XF+2XA=23, then XAXA may be written as a−bcd\tfrac{a-b\sqrt{c}}{d} for a,b,c,da,b,c,d positive integers with gcd⁡(a2,b2,c,d2)=1\gcd(a^2,b^2,c,d^2)=1 and cc squarefree. Find a+b+c+da+b+c+d.
Back to ProblemsView on AoPS