Question

In the given figure, $O$and $O^{\prime }$ are centres of two circles intersecting at $B$and$C$. $ACD$ is a straight line. Find $x$.

• A. ${130}^{\circ }$
• B. ${50}^{\circ }$
• C. ${40}^{\circ }$
• D. ${10}^{\circ }$

Answer 1

Answer: (A)

${130}^{\circ }$

$\angle AOB={130}^o...\left(Given\right)\angle AOB=2\angle ACB\Rightarrow \angle ACB={65}^o....\left(1\right).SinceACDisastraightline,\angle ACB+\angle DCB={180}^o\angle DCB={180}^o-\angle ACB={180}^o-{65}^o...\left[From\right(1\left)\right]={115}^o.Inbiggercircle,marc\left(BD\right)=2\angle BCD=2\times {115}^o={230}^{o}Now,marc\left(BD\right)+marc\left(DB\right)={360}^o\Rightarrow {230}^o+x={360}^o\Rightarrow x={130}^o.Hence,optionAiscorrect.$