17.5 In the right figure, $A B=A C=A D$, if $\angle D A C$ is $k$ times $\angle C A B$ ($k$ is a real number), then $\angle D B C$ is 
(A) $k$ times.
(B) $2 k$ times.
(C) $3 k$ times.
(D) None of the above.
(Shanghai Junior High School Mathematics Competition, 1984)
[Solution] Draw a circle with center at $A$ and radius $AB$, then by the given condition, $C, D$ lie on the circle.
Given $\angle DAC = k \angle CAB$, then $\overparen{DC} = k \overparen{BC}$.
Thus, $\angle DBC = k \angle BDC$ (by the inscribed angle theorem). Therefore, the answer is (A).