question_answer

In the given figure above,\[\angle \mathbf{AOB}=\mathbf{4}{{\mathbf{8}}^{{}^\circ }}\], AC and OB Intersect each other at right angles. What is the measure of\[\angle \mathbf{OBC}\] (where, O is the centre of the circle)?

A)  \[{{44}^{{}^\circ }}\]                       

B)  \[{{46}^{{}^\circ }}\]             

C)  \[{{66}^{{}^\circ }}\]       

D)  \[{{78.5}^{{}^\circ }}\]

Correct Answer: C

Solution :

(c): Single, angle subtentd on the circumference is half of the angle subtend on center. \[\therefore \]\[\angle ACB=\frac{1}{2}\angle AOB\] \[=\frac{1}{2}\times {{48}^{{}^\circ }}={{24}^{{}^\circ }}\] In \[\Delta MCB,\] \[\angle C+\angle B+\angle M={{180}^{{}^\circ }}\] \[\Rightarrow \]\[{{24}^{{}^\circ }}+\angle B+{{90}^{{}^\circ }}={{180}^{{}^\circ }}\] \[\therefore \]\[\angle B={{66}^{{}^\circ }}\]