What is the value of \((2^0-1+5^2+0)^{-1}\times 5\)? $$\textbf{(A) }-125\qquad\textbf{(B) }-120\qquad\textbf{(C) }\dfrac15\qquad\textbf{(D) }\dfrac5{24}\qquad\textbf{(E) }25$$
Tags: exponents,indices,powers,simplification,arithmetic-operations,order-of-operations
Source: AMC 12 2015 A Q1
Elo Rating: 1438.88
Circle \(C_1\) has its center \(O\) lying on circle \(C_2\). The two circles meet at \(X\) and \(Y\). Point \(Z\) in the exterior of \(C_1\) lies on circle \(C_2\) and \(XZ=13\), \(OZ=11\), and \(YZ=7\). What is the radius of circle \(C_1\)? $$ \textbf{(A)}\ 5\qquad\textbf{(B)}\ \sqrt{26}\qquad\textbf{(C)}\ 3\sqrt{3}\qquad\textbf{(D)}\ 2\sqrt{7}\qquad\textbf{(E)}\ \sqrt{30} $$
Tags: circles,coordinate-geometry,geometry,pythagorean-theorem,distance
Source: AMC 12 2012 A Q16
Elo Rating: 1516.00