Question

What is the relation between $\widehat{BC}$ and $\widehat{AD}$?

• A. $\widehat{BC}>\widehat{AD}$
• B. $\widehat{BC}<\widehat{AD}$
• C. $\widehat{BC}=\widehat{AD}$
• D. $\widehat{BC}=2\widehat{AD}$

Answer 1

The correct option is C

$\widehat{BC}=\widehat{AD}$

Given: $\angle AOB={90}^{\circ }$

$\angle COD={90}^{\circ }$

Now, $\angle BOC=180-\angle AOB={180}^{\circ }-{90}^{\circ }={90}^{\circ }$

and $\angle AOD=180-\angle COD={180}^{\circ }-{90}^{\circ }={90}^{\circ }$

$\Rightarrow \widehat{BC}$ subtends ${90}^{\circ }$ at the centre and $\widehat{AD}$ also subtends ${90}^{\circ }$ at the centre.

We know that equal arcs subtends equal angles at the centre,

so, $\widehat{BC}=\widehat{AD}$