question_answer

In a circle with centre O, AOC is a diameter of the circle, BD is a chord and OB and CD are joined. If \[\angle AOB=130{}^\circ ,\] then \[\angle BDC=?\]

A)  \[30{}^\circ \]                         

B)  \[25{}^\circ \]

C)  \[50{}^\circ \]                         

D)  \[60{}^\circ \]

Correct Answer: B

Solution :

            \[\angle AOB+130{}^\circ \] \[\Rightarrow \]   \[\angle BOC=180{}^\circ -\angle AOB\]                         \[=50{}^\circ \]             \[\angle BDC=\frac{1}{2}\angle BOC\]                         \[=\frac{1}{2}\times 50{}^\circ =25{}^\circ \]