Geometry Problem 941: Circles Tangent Externally, Tangent, Secant, Proportion, Angle. Level: High School, College, Mathematics Education

As illustrated, circles O and Q are tangent at A. Secants BCD and BEF are drawn so that CE and DF are tangent to circle Q at E and F, respectively. BA extended meets DF at G, Prove that (1) , (2) angle BAC = angle DAG.